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.
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