1. The equation y= mx + b is a linear relationship.
y is the dependent vairable and the output. For example, y could be the distance that someone could walk in 10 seconds.
m is the rate. For example, Henri's rate for walking is 1 meter per second.
x is the independent variable and input. For example, x could be the time that someone could walk in 1 mile.
b is the y-intercept. For example, b could be a head start in a race.
2a. A table or graph for a linear relationship can be used to solve a problem. For a table, you would look at the x and y columns and find the relationships. Then you would change the variables and solve the problem.
b. I have used an equation to solve a problem by substituting the variables with the information that I have, and then solve. Equations can also be used to check if the answer to a problem is correct by putting the answer on one side and putting the problem on the other and then solve.
Sunday, June 6, 2010
1. On a graph, a linear relationship would make a straight line. Also b in this equation is equal to the y intercept. The y intercept is where the line on a graph intersects with the y axis. M is the coefficient and represents the rate of change.
2a. It can be used to solve a problem by showing you the pattern in the numbers otherwise known as a linear equation. On a graph, you could tell if it was linear by looking to see if it makes a straight line. I can look up an x value and determine the corresponding y value. In a table, you would see a pattern in the numbers; either increasing or decreasing.
2b. I have used an equation to solve a problem such as Emile and Henri's walking rate. Emile’s equation for walking y=2.5x and Henri’s equation for walking y=x+45. I wanted to see who made it to 75 meters first. So I plugged in 75 for both equations as the y value. Then, I worked backwards. For Emile's equation, 75/2.5 and got 30 seconds. For Henri's equation, 75-45 and got 30 seconds so they both get to 75 at the same time.
2a. It can be used to solve a problem by showing you the pattern in the numbers otherwise known as a linear equation. On a graph, you could tell if it was linear by looking to see if it makes a straight line. I can look up an x value and determine the corresponding y value. In a table, you would see a pattern in the numbers; either increasing or decreasing.
2b. I have used an equation to solve a problem such as Emile and Henri's walking rate. Emile’s equation for walking y=2.5x and Henri’s equation for walking y=x+45. I wanted to see who made it to 75 meters first. So I plugged in 75 for both equations as the y value. Then, I worked backwards. For Emile's equation, 75/2.5 and got 30 seconds. For Henri's equation, 75-45 and got 30 seconds so they both get to 75 at the same time.
Math Reflection 2 Pg. 45
1. y=mx+b is a linear equation that can be used to help set up a real linear equation.
M is the rate. For example it could be 7 for the amount of minutes it takes to run 1 mile.
Y is the dependent variable or the output. For example it could be the amount of miles you run in a certain time.
X is the independent variable or input. For example y could be the number of hours/time.
B is the y-intercept. B is the number added on to m times x.
2a. A table of graph for a linear relationship can be used to solve a problem. A table can be used by looking at the y and x columns and seeing if there is any pattern. If there is no patterns look in between each row for each column. Record them down and if you can make a ratio do it. If the ratios for each column equal each other that means the table is linear. The graph can be used by if the line is straight or not. If the line is straight that means the graph is linear. If the line is not straight that means the graph is not linear.
2b. I have used a equation to solve a problem before. I wanted to know how long it would take me to run 3 miles. I knew that I can run a mile in 6 minutes 30 seconds. My first equation was t=6.5m. T is minutes taken to run. M is the amount of miles. Then I realized that I would probably be off by 2 minutes because my rate would be slower so I added 2 minutes. My new equation is 6.5m+2=t. That means it would take me 21 minutes and 30 seconds to run 3 miles.
msa mr 2
1. Linear relationships are represented in the equation y=mx+b. All the letters in this equation are variable representing something.
In this equation, m stands for the rate of change, and also for the coefficient of x. An example of m is a person walking 2.5 meters per second.Y is the dependent variable. An example of y is when someone walks 2 meters per second, the 2 meters ids the dependent variable, or the y.X is the independent variable. In most cases, time is the independent variable.B is the y-intercept. The y-intercept is the point where the line crosses the y axis in a graph, and when the dependent variable in a table is 0. If this equation was put into a graph, there would be a straight line representing it. If it was in a table, there would be a steady increase of the numbers.
2a. A table and a graph of a linear equation can both be used to solve a problem. A table can be used because you can used the numbers in the table to figure out the answer. In a table, you can easily see the relationship between x and y, the y-intercept, and the rate of change. If you substitute the x and y in, you can solve the problem. You can solve a problem with a graph because you can go on the x or y axis along to the line, the see on the other line what the number is.
2b. You can use an equation to solve a problem because you substitute the numbers you have(the x, the y, the coefficient and the y-intercept, all the information you have) Then you solve the equation, keeping in mind order of operations, and get the answer.
MSA math Reflection 2
Math Reflection 2:
1) Y=mx +b is an equation that you can use for, pretty much, any linear relationship which would make a perfectly straight line on a graph. Y is the dependent variable or the “output” like the distance in miles or feet etc. (on the y axis.) M is the rate of change which is a unit rate (depending on how much time.) For example, M could be 5 miles per hour or 2 meters per second etc. Next is X. X is the independent variable or the “input”, like time (like seconds, minutes, hours etc. on the X axis). The next variable is B. B stands for the y intercept (a point on a graph when it crosses the y axis or when the y axis is 0 on a table). With any situation you use, this equation should be a linear equation, meaning that it should make an even, straight line on a graph.
2) A: You can use a table to solve a problem for a linear relationship to solve a problem by looking at the information that the table gives by looking at the X and Y columns to see what the relationship between them is. Then, you can keep adding to the table to solve any situation or equation. For example: If you had 2 meters on the y axis and 1 second on the x axis then you could figure out how many seconds it would take you 4 meter by just adding more seconds until you get to 4 (so it would be 4 meters in 2 seconds). You can use the graph to solve any problem for a linear relationship by looking at the linear line that it shows and keep going up or down the line to find your answer you are looking for. So it you were wanting to find how many seconds in 5 meters you would just drag you finger up the y axis until you got to 5 and then go across until you found how many seconds it took for 5 meters.
B: I have used an equation to solve a problem by substituting out the variables and plugging in the numbers that they give you to solve the problem or any problem. For example, if y=3x-7, so Y was the miles and x would be the number of minutes. If they asked me how many miles can so and so go in 6 minutes, I would do y=3*6-7 so 3*6=18, and 18-7= 11. So, my answer would be so and so can go 11 miles in 6 minutes.
1) Y=mx +b is an equation that you can use for, pretty much, any linear relationship which would make a perfectly straight line on a graph. Y is the dependent variable or the “output” like the distance in miles or feet etc. (on the y axis.) M is the rate of change which is a unit rate (depending on how much time.) For example, M could be 5 miles per hour or 2 meters per second etc. Next is X. X is the independent variable or the “input”, like time (like seconds, minutes, hours etc. on the X axis). The next variable is B. B stands for the y intercept (a point on a graph when it crosses the y axis or when the y axis is 0 on a table). With any situation you use, this equation should be a linear equation, meaning that it should make an even, straight line on a graph.
2) A: You can use a table to solve a problem for a linear relationship to solve a problem by looking at the information that the table gives by looking at the X and Y columns to see what the relationship between them is. Then, you can keep adding to the table to solve any situation or equation. For example: If you had 2 meters on the y axis and 1 second on the x axis then you could figure out how many seconds it would take you 4 meter by just adding more seconds until you get to 4 (so it would be 4 meters in 2 seconds). You can use the graph to solve any problem for a linear relationship by looking at the linear line that it shows and keep going up or down the line to find your answer you are looking for. So it you were wanting to find how many seconds in 5 meters you would just drag you finger up the y axis until you got to 5 and then go across until you found how many seconds it took for 5 meters.
B: I have used an equation to solve a problem by substituting out the variables and plugging in the numbers that they give you to solve the problem or any problem. For example, if y=3x-7, so Y was the miles and x would be the number of minutes. If they asked me how many miles can so and so go in 6 minutes, I would do y=3*6-7 so 3*6=18, and 18-7= 11. So, my answer would be so and so can go 11 miles in 6 minutes.
1) Linear relationships are represented by the equation y=mx+b.
m stands for the rate of change and the coefficient of x. For example, a walking rate could be 2 meters per second.
y is the dependent variable, like distance, or the output.
x is the independent variable, like time, or the input.
b is the y-intercept, or the point where the line crosses the y axis on a graph or when 0 is y in a table.
If you were to plot the equation y=mx+b (when the letters are numbers) then the line should be a straight line, meaning it’s linear.
2a) You can use a table or graph for a linear relationship to solve a problem. You can use the information on a table to solve a problem. You can use a graph because if the line is linear, you can use the scale marks and the information on it to solve a problem.
2b) I have used an equation to solve a problem in many ways. I have used the guess and check method using equations by putting a number that is an estimate and seeing if it works. I have also learned to find a number that intersects 2 equations by having 2 equations on either side of an equal sign. For example, in problem 3.5, there were two equations: E=825+3.25n and I=8.20n. Then I did 825+3.25n=8.20n then just solved the equation.
math reflection
Math Reflection
1. Linear relationships can be represented by the equation. y =mx + b. This equation is actually a form of a linear relationship. First the y in the equation (y=mx + b) represents the dependent variable. This is the variable that changes depending how the other variable increases or decreases. In a graph situation the y variable is represented by the y axis. For example in a situation the y variable would be distance. Next, the m in the equation (y=mx + b) represents the rate. This is how many times something happens per unit of time. For example: in the equation, y= 3x + 50, 3 would be the m variable. This is because 3 is the rate, no matter what number you plug in for x, it will always be multiplied by 3. Next, the x in the equation (y=mx + b) represents the dependent variable. This is the variable that increases at a steady rate. The depending variable changes depending on what the independent variable is. On a graph the independent variable is represented on the x axis. In a situation, an example of the independent variable would be time. So if the independent variable is distance and the dependent variable is time, the distance would change depending on how the time changes. Lastly, the b in the equation (y=mx + b) represents the y- intercept. The y- intercept is the point where the line in a graph crosses the y axis. For Example: in this equation, y= 3x + 50, 50 would be the y intercept. This is because 50 is the point where the line intercepts the y axis. This is how a linear relationship is represented by the equation y=mx + b.
2a. A table for a linear relationship could be used to solve a problem by using the information provided in the table. You can see the relationship between numbers in a table along with the rate, y intercept and the independent and dependent variables. You could therefore use that information to solve the problem. A graph for a linear relationship could be used to solve a problem by provided a different and some ways more clear way of the information. Some things you could see easier in a graph than a table to help you solve the problem.
b. you could use an equation for a linear relationship to solve a problem by substituting the numbers you have to solve the problem for the variables in the equation. after the numbers are substituted you follow the order of operations to solve the equation and then check your answer.
MSA MR 2
1. We learned that the equation y=mx+b is a very important equation to know. We learned y is the dependant variable, m is the rate, b is the y intercept and x is the independant variable. The y intercept is the point that crosses or intersects with the y axis on a graph.
2a.)For a table, you can use it to solve a problem by seeing the constant rate and then put them in the problem you are trying to solve. For a graph you count the intervals between the points. Then, the intervals you found is your constant rate that you have in your equation or the variable m.
2b.) I have used an equation to solve a problem, by substituting the variable, with what ever number you are using. I used an equation in problem 2.3, where when I wanted to find out how much 100 shirts cost; I replace the variable with 100. 49+n, then I replaced n with 100, 40+100=$149. That’s how I used equation to solve a problem.
2a.)For a table, you can use it to solve a problem by seeing the constant rate and then put them in the problem you are trying to solve. For a graph you count the intervals between the points. Then, the intervals you found is your constant rate that you have in your equation or the variable m.
2b.) I have used an equation to solve a problem, by substituting the variable, with what ever number you are using. I used an equation in problem 2.3, where when I wanted to find out how much 100 shirts cost; I replace the variable with 100. 49+n, then I replaced n with 100, 40+100=$149. That’s how I used equation to solve a problem.
1. A relationship is linear by the equation y=mx+b. This equation means that y, or the dependent variable or the answer, is found doing m times x plus b. M is the variable for the rate of the problem. An example from Problem 2.1, Henri's walking rate was 2 meters per second. X is the independent variable or input. B is the variable for the y-intercept, the point on a graph where the graphed data line crosses the y-axis. So in this equation the rate times the input plus the y-intercept equals a linear relationship.
2.a. A table can be used to solve a problem in a linear relationship by using the other information described in the problem to be put into a table. The data from the table will help with solving the problem because the table is made according to the problem. When a graph is used to solve the problem, all you need to do after creating the graph from the data and/or table, is to use that information from the axes and linear line to be context clues for the problem.
b. An equation is simple for solving a problem in a linear relationship because all you need to do is substitute the variables from the linear equation, y=mx+b, with the data in the problem. For example, is m=2, x=3, and b=13 (determined from the information of the problem), you now solve it. This becomes y=2•3+13, so y is 18.
2.a. A table can be used to solve a problem in a linear relationship by using the other information described in the problem to be put into a table. The data from the table will help with solving the problem because the table is made according to the problem. When a graph is used to solve the problem, all you need to do after creating the graph from the data and/or table, is to use that information from the axes and linear line to be context clues for the problem.
b. An equation is simple for solving a problem in a linear relationship because all you need to do is substitute the variables from the linear equation, y=mx+b, with the data in the problem. For example, is m=2, x=3, and b=13 (determined from the information of the problem), you now solve it. This becomes y=2•3+13, so y is 18.
Saturday, June 5, 2010
1. In the equation y = mx + b, the rate is expressed by the variable “m”. The y-intercept, which is the point where the line crosses the y axis on a graph or when y equals 0 in a table, is expressed by the variable “b”. Also, the y intercept is what is added to the rate or coefficient. Next, the dependant variable, for example, distance, is expressed by “y”. The coefficient is the number that multiplies a variable in an equation. Finally, the independent variable, for example, time, is expressed by the variable “x”.
2. a) A table or graph for a linear relationship can be used to solve a problem by filling in the table or graph and finding the numbers you need to do the problem. For example, if Lucy buys 20 apples for $4.00 each, and you need to figure out how much each apple cost, you can use a table and/or a graph. To use a table, take the equation and rate to find the numbers used in the table. Then continue the table to find your answer. The x column on the table would show that it is $5 for one apple. You can do the same thing with a graph, but just extend the line on the graph until you have your answer.
Friday, June 4, 2010
MSA MR 2
1. If two subjects had a linear relationship and were put into a graph, the line created by the information following the subjects would form a perfectly straight line, and if they were put into a table, their rates would go up at a constant/steady rate. Also, with equations you could form a linear relationship as well. In the equation y = mx + b, the letters are variables that represent different things in an equation.
The y in this equation is the dependent variable, the output. For example, distance is typically a dependant variable in an equation.
The x in this equation is the independent variable, the input. For example, time is typically the independent variable in an equation.
The b in this equation is the y-intercept in an equation/a head start. For example, in running a business, before you begin paying for each item individually, other things such as the mortgage, heat bills, water bills, etc., so your y-intercept would probably be in the hundreds.
The m in this equation is the rate of an equation. For example, someone might have a walking rate of 2.5 meters per second, so their rate would 2.5 mps.
b.) I have used an equation to solve a problem by substitutung the numbers that I need to use to solve that problem for the variable(s)in that equation, and this is how I have used an equation to solve a problem.
Thursday, June 3, 2010
1) A linear relationship is a functional relationship between an independent and dependent variable, that is represented on a graph by a straight line
In the equation y = mx + b, each letter is a variable.
y is the dependant variable. The dependant variable is a variable whose value relies upon the independent variable. It can also be thought of as the y axis—the vertical axis on a graph.
x is the independent variable. The independent variable does not depend upon any other variable to determine its value.
m represents the rate. The rate is basically the amount of any given unit of the y axis, relative to any given unit of time (the x axis).
b symbolizes the y-intercept: the point at which the y axis is crossed. Basically, the y-intercept is where the line begins.
Let’s say the graph is representing how much it costs to buy videos from a rental store. The store charges $10.00, plus $5.00 per video.
y (the dependant variable) = The total cost of the videos
x (the independent variable) = How many videos are purchased
m (the rate) = $5.00, because it is $5.00 per video
b (the y-intercept) = $10.00, because that is how much money is charged regardless of how many videos are bought.
So if someone tried to rent 10 videos, the equation would become:
y = 5 * 10 + 10
This becomes y = $60.00
In other words, renting 10 videos costs $60.00.
2)
A. A table can be created to use to solve a problem because the pattern becomes very plain and obvious to see once the table is filled out. This makes following the pattern easier, so more and more data can be added as needed.
A graph can be used because plotting the points on the x axis and the y axis make certain aspects of the equation easier to understand—such as what the y-intercept is and where it is located.
Both methods are good for people who learn visually.
B) I often use equations to solve problems, as seen above on problem A. Equations are simple because the formula is laid out right in front of you—all you have to do is plug in the numbers where the variables are.
The equation in problem A was y = mx + b
m = $5.00
x = 10
b = $10.00
Therefore, the equation becomes y = 5 * 10 + 10
This becomes y = 50 + 10
Which ends as y = 60
By Grace T
In the equation y = mx + b, each letter is a variable.
y is the dependant variable. The dependant variable is a variable whose value relies upon the independent variable. It can also be thought of as the y axis—the vertical axis on a graph.
x is the independent variable. The independent variable does not depend upon any other variable to determine its value.
m represents the rate. The rate is basically the amount of any given unit of the y axis, relative to any given unit of time (the x axis).
b symbolizes the y-intercept: the point at which the y axis is crossed. Basically, the y-intercept is where the line begins.
Let’s say the graph is representing how much it costs to buy videos from a rental store. The store charges $10.00, plus $5.00 per video.
y (the dependant variable) = The total cost of the videos
x (the independent variable) = How many videos are purchased
m (the rate) = $5.00, because it is $5.00 per video
b (the y-intercept) = $10.00, because that is how much money is charged regardless of how many videos are bought.
So if someone tried to rent 10 videos, the equation would become:
y = 5 * 10 + 10
This becomes y = $60.00
In other words, renting 10 videos costs $60.00.
2)
A. A table can be created to use to solve a problem because the pattern becomes very plain and obvious to see once the table is filled out. This makes following the pattern easier, so more and more data can be added as needed.
A graph can be used because plotting the points on the x axis and the y axis make certain aspects of the equation easier to understand—such as what the y-intercept is and where it is located.
Both methods are good for people who learn visually.
B) I often use equations to solve problems, as seen above on problem A. Equations are simple because the formula is laid out right in front of you—all you have to do is plug in the numbers where the variables are.
The equation in problem A was y = mx + b
m = $5.00
x = 10
b = $10.00
Therefore, the equation becomes y = 5 * 10 + 10
This becomes y = 50 + 10
Which ends as y = 60
By Grace T
MSA MR 2
1.) There is a linear relationship represented by y=mx+b. In the equation, y means the dependent variable or the y-axis, on a graph, and m means the rate. Also, b means the y-intercept, and x means the dependent variable or the x-axis, on a graph. An example that shows y=mx+b, is:
c= cost in dollars t= number of shirts
c=5t+20
If you wanted to buy 30 shirts then:
c=5*30+20
c=150+20
c=170
In this example, 5, is the rate, t or 30, is the independent variable, and 20 is the y-intercept.
2 a.) A table and a graph can be used to solve a problem. A table can be used by filling in a table with the information and then by continuing the pattern.
The Cost of Shirts
| TOTAL NUMBER OF SHIRTS | COST IN DOLLARS |
| 10 | 70 |
| 20 | 120 |
| 30 | 170 |
A graph can be used to solve a linear equation because you plot the the data and continue the pattern. When you plot the data for the linear equation, you would be able to see the linear relationship on the graph because there would be a straight line.
2 b.) I used an equation to solve a problem by substituting the variables for the numbers.
EXAMPLE:
c= cost t= total number of shirts
c=5t+20
If you bought 20 shirts then:
c=5*20+20
c=100+20
c=120
MSA MR 2
1. I know that in a linear relationship represented by an equation of the form y=mx+b is that m represents the rate, x represents the independent variable (input), b represents the y intercept (the number that you start of with), and y represents the dependent variable (output). For example, m could be the amount of meters traveled in one second which would be the rate, x could be the amount of hours you multiply by the amount of meters traveled in a second, b could be that maybe you were racing somebody and you had a head start of 30 meters which would make the 30 meters the y intercept, and y would be the the final answer after you multiply the the rate by the number of hours and add 30 to it.
2.
a. A graph for a linear relationship can be used to solve a problem by seeing the rate it goes up by. You can see this rate by the data points on the graph. For example, you wanted to know how many meters a person walks in 10 seconds and they have a walking rate of 2 meters per second. So you go to 10 seconds on the x axis because its the independent variable, and you multiply it by 2 and you figure out that since for all of the other data points that you multiply the number of seconds by 2 to get the meters per second which makes it 20 meters in 10 seconds. A table for a linear relationship can be used to solve a problem by seeing the rate it goes by on the table in numbers. For example, you walk 2 meters per second and you want to know how many meters you can go in 5 seconds. So you multiply 2 meters by 5 and you get 10 meters in 5 seconds.
b. I have used an equation to solve a problem by multiplying the independent variable by the rate to get the dependent variable. If you walk 2 meters per second and you want to know how many meters you van go in 6 seconds and your equation when distance in meters is d and time in seconds is t is d=2t, you multiply 2 by 6 and you get 12 meters in 6 seconds.
2.
a. A graph for a linear relationship can be used to solve a problem by seeing the rate it goes up by. You can see this rate by the data points on the graph. For example, you wanted to know how many meters a person walks in 10 seconds and they have a walking rate of 2 meters per second. So you go to 10 seconds on the x axis because its the independent variable, and you multiply it by 2 and you figure out that since for all of the other data points that you multiply the number of seconds by 2 to get the meters per second which makes it 20 meters in 10 seconds. A table for a linear relationship can be used to solve a problem by seeing the rate it goes by on the table in numbers. For example, you walk 2 meters per second and you want to know how many meters you can go in 5 seconds. So you multiply 2 meters by 5 and you get 10 meters in 5 seconds.
b. I have used an equation to solve a problem by multiplying the independent variable by the rate to get the dependent variable. If you walk 2 meters per second and you want to know how many meters you van go in 6 seconds and your equation when distance in meters is d and time in seconds is t is d=2t, you multiply 2 by 6 and you get 12 meters in 6 seconds.
1. There is a linear relationship in the form of the equation y=mx+b. A linear relationship is when two variables form a constant rate of change. Y is the unknown, x is the unknown, m is the coefficient of x (the coefficient is the number that multiplies a variable in an equation) , and b is the y-intercept (the y-intercept is the point where the line crosses the y-axis). For example: if m=6 and b=5, the equation would be y=6x+5. Assuming that x=2, y would equal 17 because
y=6(2)+5.
y=12+5
y=17
check:
17=6(2)+5
17=12+5
17=17
If you had the value of y, which is 17, and needed to find the value of x, you would have the equation
17=6x+5.
-5 -5
-------
12=6x
/6 /6
-----
2=x
check:
17=6(2)+5
17=12+5
17=17
2.a. A table or graph can be used to solve a problem by evaluating the data. For a table, you can write an equation from the given data.
Prices for Tom's Bagels
|---------------------|----|----|----|----|----|----|
|# of Bagels....... | 1 | 2 | 3 | 4 | 5 | 6 |
|---------------------|----|----|----|----|----|----|
|Cost in cents.... |.25 |.50 |.75 |1.00|1.25|1.50|
|---------------------|----|----|----|----|----|----|
n=number of bagels c=cost in cents
c=.25n
A graph for a linear relationship can be used to solve a problem by evaluating the graph and finding plotted points on it that run within the linear line.
2.b. I have used an equation to solve a problem many times before. When some of my friends and I sold cupcakes at the seventh grade lunch, we estimated how much money we would raise for Haiti depending on how many cupcakes we made and depending on the price of each cupcake. If the cupcake was .25 cents and we made 75 cupcakes, we would raise $18.75. The equation is:
n=number of cupcakes m=money raised in dollars and/or cents
m=.25n
y=6(2)+5.
y=12+5
y=17
check:
17=6(2)+5
17=12+5
17=17
If you had the value of y, which is 17, and needed to find the value of x, you would have the equation
17=6x+5.
-5 -5
-------
12=6x
/6 /6
-----
2=x
check:
17=6(2)+5
17=12+5
17=17
2.a. A table or graph can be used to solve a problem by evaluating the data. For a table, you can write an equation from the given data.
Prices for Tom's Bagels
|---------------------|----|----|----|----|----|----|
|# of Bagels....... | 1 | 2 | 3 | 4 | 5 | 6 |
|---------------------|----|----|----|----|----|----|
|Cost in cents.... |.25 |.50 |.75 |1.00|1.25|1.50|
|---------------------|----|----|----|----|----|----|
n=number of bagels c=cost in cents
c=.25n
A graph for a linear relationship can be used to solve a problem by evaluating the graph and finding plotted points on it that run within the linear line.
2.b. I have used an equation to solve a problem many times before. When some of my friends and I sold cupcakes at the seventh grade lunch, we estimated how much money we would raise for Haiti depending on how many cupcakes we made and depending on the price of each cupcake. If the cupcake was .25 cents and we made 75 cupcakes, we would raise $18.75. The equation is:
n=number of cupcakes m=money raised in dollars and/or cents
m=.25n
Sunday, May 2, 2010
Daily Scribe
Friday in class we continued to work on how to solve equations. Mostly, we focused on equations that have negative numbers in them, or you have to use a negative number in order to solve it. For example:
7+3x=5x+13
When you are solving and equation like this you have to remember that whatever you do to one
side, you have to do to the other in order to maintain balance.
For example:
7 + 3x = 5x + 13
-7 -7 Subtract & from each side
_____________
3x = 5x + 6
Now, you have to make the equation so one side is equal to x and the other to a number.
7 + 3x = 5x + 13
-7 -7 Subtract 7 from each side
______________
3x = 5x + 6
-5 -5 subtract 5 from each side
_________________
-2x = 6
/ -2 / -2 divide by -2 on each side
Now you have a negative number one one side and a positive on the other. You still have to get one side to x so you would divide -2 by -2 and 6 by -2 in order to get the answer.
__________________
x= -3
Now that you have solved the equation you want to check your answer. You do that by plugging in the number you figured out that x was, anywhere in the equation where you see there is an x. Then you follow the order of operations in order to solve the equation. In the end, if the answer is correct both numbers on each side of the equal sign should be the same.
For example:
The equation was: 7+3x=5x+13
The answer we got is: x=-3
*reminder- the order of operations is PE
MD
AS
or Parentheses Exponent Multiplication Division Addition Subtraction
Now check to see if the answer is correct.
7+3(-3)=5(-3)+13
7+ (-9)= (-15)+13
-2 = -2
Thursday, April 29, 2010
Wednesday, April 28, 2010
Daily Scribe Tues. April 27
Today we learned how to find an answer to an equation using coins and pouches. With these problems, you find how many coins are in a pouch. For example...
C= coins P=pouches
cccccccccc=pppcccc
So first you put
3p (3 pouches)+4 (the 4 coins on the side it was with) =10 (total coins on the other side)
Then you do
3p+4=10
-4 -4
__________
3p=6
So you subtract 4 from 4, or in any problem, the number of coins on the pouches side. Then you'd subtract 4 from 10, or 4 from the 10 coins on the other side.
You see after you do the first steps you see 3p=6
So then you'd do
3p=6
________
3 3
_______
1p= 2
So 3 divided by 3 is 1, so you have 1 pouch. Then you do 6 divided by 3 and get 2, so there's 2 coins per pouch.
This is what we learned in class.
C= coins P=pouches
cccccccccc=pppcccc
So first you put
3p (3 pouches)+4 (the 4 coins on the side it was with) =10 (total coins on the other side)
Then you do
3p+4=10
-4 -4
__________
3p=6
So you subtract 4 from 4, or in any problem, the number of coins on the pouches side. Then you'd subtract 4 from 10, or 4 from the 10 coins on the other side.
You see after you do the first steps you see 3p=6
So then you'd do
3p=6
________
3 3
_______
1p= 2
So 3 divided by 3 is 1, so you have 1 pouch. Then you do 6 divided by 3 and get 2, so there's 2 coins per pouch.
This is what we learned in class.
Monday, April 26, 2010
Daily Scribe for 4/26/10
Today in class, we began to focus, among other things, upon mantaining an equivalent value between two things.
In other words, we were learning how to keep a balance.
We did a labsheet involving "gold coins" and "diplomatic pouches". The idea was that each pouch contained a certain number of gold coins. On one side, there was a certain amount of gold coins, and perhaps a pouch or two. On the other side was a diferent amonut of coins, and possibly pouches. By eliminating the same number of coins and pouches on each side, we were eventually able to come up with one pouch, and however many gold coins.
For pouches, I am going to use X's. For coins, I am going to use Y's.
************************************************************************
A) y y y y y y y y y y = x x x y y y y
10 y's = 3 x's plus 4 y's. First, you can eliminate 4 y's from each side. The new equation will be:
y y y y y y = x x x
So, 6 y's = 3 x's. This means 1 x = 2 y's.
Therefore, if x means pouches and y means coins, there are 2 coins per pouch.
B) x x x y y y = y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y
3 x's plus 3 y's = 30 y's, so you can eliminate 3 y's from each side.
x x x = y y y y y y y y y y y y y y y y y y y y y y y y y y y
3 x's = 27 y's, so 1 x = 9 y's. Therefore, there are 9 coins per pouch.
B2) x x y y y y = y y y y y y y y y y y y
2 x's and 4 y's = 12 y's. This means that 4 y's can be taken from each side.
x x = y y y y y y y y
2 x's = 8 y's. This means that 1 x = 4 y's. In other words, there are 4 coins per pouch.
B3) x x x = x x y y y y y y y y y y y y y
3 x's = 2 x's and 12 y's, so this time 2 x's can be eliminated from each side.
x = y y y y y y y y y y y y
x = 12 y's, so there are 12 coins per pouch.
B4) x x x y y y = x x y y y y y y y y y y y y
3 x's and 3 y's equals 2 x's and 12 y's. First take 2 x's away from each side.
x y y y = y y y y y y y y y y y y
1 x and 3 y's = 12 y's, so now 3 y's can be taken away from both sides as well.
x = y y y y y y y y y
x = 9 y's. Therefore, there are 9 coins per pouch.
B5) x x y y y y y y y y y y y y y y y y y y y y y = x x x x x y y y
2 x's and 21 y's = 5 x's and 3 y's. First take away 2 x's from each side.
y y y y y y y y y y y y y y y y y y y y y = x x x y y y
21 y's = 3 x's and 3 y's, so now eliminate 3 y's on each side.
y y y y y y y y y y y y y y y y y y = x x x
18 y's = 3 x's, so 6 y's = 1 x. There are 6 coins per pouch.
****************************************************************
That was a run-through of pretty much everything we covered in class today. Hopefully, you have now gained a clearer understanding of equivalent balances!
Signed,
Grace T :)
In other words, we were learning how to keep a balance.
We did a labsheet involving "gold coins" and "diplomatic pouches". The idea was that each pouch contained a certain number of gold coins. On one side, there was a certain amount of gold coins, and perhaps a pouch or two. On the other side was a diferent amonut of coins, and possibly pouches. By eliminating the same number of coins and pouches on each side, we were eventually able to come up with one pouch, and however many gold coins.
For pouches, I am going to use X's. For coins, I am going to use Y's.
************************************************************************
A) y y y y y y y y y y = x x x y y y y
10 y's = 3 x's plus 4 y's. First, you can eliminate 4 y's from each side. The new equation will be:
y y y y y y = x x x
So, 6 y's = 3 x's. This means 1 x = 2 y's.
Therefore, if x means pouches and y means coins, there are 2 coins per pouch.
B) x x x y y y = y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y
3 x's plus 3 y's = 30 y's, so you can eliminate 3 y's from each side.
x x x = y y y y y y y y y y y y y y y y y y y y y y y y y y y
3 x's = 27 y's, so 1 x = 9 y's. Therefore, there are 9 coins per pouch.
B2) x x y y y y = y y y y y y y y y y y y
2 x's and 4 y's = 12 y's. This means that 4 y's can be taken from each side.
x x = y y y y y y y y
2 x's = 8 y's. This means that 1 x = 4 y's. In other words, there are 4 coins per pouch.
B3) x x x = x x y y y y y y y y y y y y y
3 x's = 2 x's and 12 y's, so this time 2 x's can be eliminated from each side.
x = y y y y y y y y y y y y
x = 12 y's, so there are 12 coins per pouch.
B4) x x x y y y = x x y y y y y y y y y y y y
3 x's and 3 y's equals 2 x's and 12 y's. First take 2 x's away from each side.
x y y y = y y y y y y y y y y y y
1 x and 3 y's = 12 y's, so now 3 y's can be taken away from both sides as well.
x = y y y y y y y y y
x = 9 y's. Therefore, there are 9 coins per pouch.
B5) x x y y y y y y y y y y y y y y y y y y y y y = x x x x x y y y
2 x's and 21 y's = 5 x's and 3 y's. First take away 2 x's from each side.
y y y y y y y y y y y y y y y y y y y y y = x x x y y y
21 y's = 3 x's and 3 y's, so now eliminate 3 y's on each side.
y y y y y y y y y y y y y y y y y y = x x x
18 y's = 3 x's, so 6 y's = 1 x. There are 6 coins per pouch.
****************************************************************
That was a run-through of pretty much everything we covered in class today. Hopefully, you have now gained a clearer understanding of equivalent balances!
Signed,
Grace T :)
Thursday, April 15, 2010
Math Reflection 1
1. In a linear relationship, the dependent variable changes as the independent variable changes. A linear relationship is when the variables go up at a steady rate. For example, if someone starts off with $100 at the beginning of the week, then is left with $80 the next and $60 the next and so on, then the money (dependent variable) is decreased at a steady rate, as the days (independent variable) is also decreasing at a steady rate. The rest of the week would look like this:
Number of Days – Money Left
0 - 100
1 - 80
2 - 60
3 - 40
4 - 20
5 - 0
2. The pattern of change for a linear relationship shows up in a table if the numbers change by decreasing or increasing at a certain rate. For example, if the table:
Miles walked-Time in minutes
2 - 20
3 - 30
4 - 40
5 - 50
The number of miles increases by 1 mile every 10 minutes, so the pattern of change would be 1 mile
The pattern of change for a linear relationship shows up in a graph is the data points are connected in a straight line. For example,
Number of Days – Money Left
0 - 100
1 - 80
2 - 60
3 - 40
4 - 20
5 - 0
2. The pattern of change for a linear relationship shows up in a table if the numbers change by decreasing or increasing at a certain rate. For example, if the table:
Miles walked-Time in minutes
2 - 20
3 - 30
4 - 40
5 - 50
The number of miles increases by 1 mile every 10 minutes, so the pattern of change would be 1 mile
The pattern of change for a linear relationship shows up in a graph is the data points are connected in a straight line. For example,
The pattern of changes for a linear relationship shows in an equation if the variables are being multplied of divided. Equations are usually used for linear relationships, so if data is not linear, then there usually no equation. For example, in the equation m=20w (w=weeks) (m-money left), since the variable is multiplied, it would be a linear relationship.
MSA mr 1
1) In a linear relationship, as the dependent variable changes at a constant rate, the independent variable goes up at a constant rate too. For example: If John had $100 for his snack money and spent $10 each week, both of the variables will decrease at a steady rate every time John spends $10. The dependent variable would be the number of weeks because the number of weeks depends on how much money you have. The independent variable would be the amount of money, which in this case would be $100 total. If you had a table and graph, you would see that at each week, the amount of money on the y axis would go down $10 at a constant rate.
2) The pattern in a linear relationship shows up in the table, graph, and equation and goes up, down or stays the same at a constant rate. For example, If Jen had $400 and she spent $50 a day, the table would go down at a steady rate on both the x and y axis’s.
(independent)Amount of money left / (dependent)number of days
$400 / 0
$350 / 1
$300 / 2
$250 / 3
$200 / 4
$150 / 5
$100 / 6
$50 / 7
$0 / 8
________________________________
From the table, the y axis goes down by $50 at a constant rate each day. On the x axis the number of days go up by 1 at a constant rate each day.
If the pattern is a linear relationship, the graph should go up or down or stay the same at a steady rate and make a straight line, such as the graph below. As the dependent variable changes, the independent variable also goes up, down or stays the same at a constant rate.
1) In a linear relationship, as the dependent variable changes at a constant rate, the independent variable goes up at a constant rate too. For example: If John had $100 for his snack money and spent $10 each week, both of the variables will decrease at a steady rate every time John spends $10. The dependent variable would be the number of weeks because the number of weeks depends on how much money you have. The independent variable would be the amount of money, which in this case would be $100 total. If you had a table and graph, you would see that at each week, the amount of money on the y axis would go down $10 at a constant rate.
2) The pattern in a linear relationship shows up in the table, graph, and equation and goes up, down or stays the same at a constant rate. For example, If Jen had $400 and she spent $50 a day, the table would go down at a steady rate on both the x and y axis’s.
(independent)Amount of money left / (dependent)number of days
$400 / 0
$350 / 1
$300 / 2
$250 / 3
$200 / 4
$150 / 5
$100 / 6
$50 / 7
$0 / 8
________________________________
From the table, the y axis goes down by $50 at a constant rate each day. On the x axis the number of days go up by 1 at a constant rate each day.
If the pattern is a linear relationship, the graph should go up or down or stay the same at a steady rate and make a straight line, such as the graph below. As the dependent variable changes, the independent variable also goes up, down or stays the same at a constant rate.
If you start out with $400 and every day you spend $50, all of the money would be used up by day 8. The variables form a straight line if the pattern is linear.
If you wrote out an equation it would be m=400-(50d) (m= amount of money left, d= number of days). So if you were at 2 days (you replace variable d), you would do : 400- (50 * 2)= m so if you do order of operations you would get $300 left after 2 days. Another example would be if you were at 7 days you would do: 400- (50*7)= m. M would equal $50.
In the table, graph and the equation, the linear relationship can go up, down or stay the same at a constant rate.
If you wrote out an equation it would be m=400-(50d) (m= amount of money left, d= number of days). So if you were at 2 days (you replace variable d), you would do : 400- (50 * 2)= m so if you do order of operations you would get $300 left after 2 days. Another example would be if you were at 7 days you would do: 400- (50*7)= m. M would equal $50.
In the table, graph and the equation, the linear relationship can go up, down or stay the same at a constant rate.
Wednesday, April 14, 2010
1.) Describe how the dependent variable changes as the independent variable changes in a linear relationship. Give examples.
In a linear relationship, the dependent variable changes at a constant rate as the independent variable changes. For example, If a person bikes 8 miles per hour, than in 2 hours they would have rode 16 miles. The hours are the independent variable, and the miles are the dependant variable. In this example, the dependant variable goes at a constant rate of 8 miles for every hour. This constant rate would continue and there would be 16 miles for 2 hours, then 24 miles for 3 hours, then 32 hours for 4 hours, and so on.
2.) How does the pattern of change for a linear relationship show up in a table, a graph, and an equation of the relationship?
The pattern of change for a linear relationship shows up in a table because you can see the constant rate and how the numbers change. For example, if there is a table where x went 2,3,4,5 and the y went 20, 30, 40, 50, than this would be a linear relationship. This would be a linear relationship because there is a constant rate. The constant rate for x is +1 and the constant rate for y is +10.
The pattern of change for a linear relationship, shows up in a graph, because the data points on the graph create a straight line. The graph above is a linear relationship because the rate is constant and the line is straight. For the graph above, the constant rate is, for every time that the hours increase by 1, the miles increase by 50.
For the example, look at the top of the page.
The pattern of change for a linear relationship shows up in an equation because the equation is linear as long as there are no exponents. The number in the equation shows the amount of change of the dependant variable.
For example:
t=hours d=miles
7t=d
This equation means that they are going 7 miles per hour. The 7 is the unit rate of how far they go in one hour. Since there are no exponents, the equation is a linear relationship. Also, the 7 tells you the amount of change. If the number in the equation was 8 than the person would be going faster, at 8 miles per hour.
This equation means that they are going 7 miles per hour. The 7 is the unit rate of how far they go in one hour. Since there are no exponents, the equation is a linear relationship. Also, the 7 tells you the amount of change. If the number in the equation was 8 than the person would be going faster, at 8 miles per hour.
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