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.
Sunday, June 6, 2010
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.
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