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Thinking with mathematical models

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Tamara Canales

on 29 September 2015

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Transcript of Thinking with mathematical models

Why is it helpful to use a linear model for a data set?
It is helpful because it makes complicated information look much easier. To find out how accurate the data is you can see it by the linear model, and you can calculate errors in the predictions made by the model.
How would you find the equation for a linear function in the following situations?
You are given a description of the variables in words
You are given a table of values for the variables
You are given a graph of sample data points
Strategies you can use
to solve linear equations
500= 5x + 245 (solving for x): When you solve for x first you should get rid of the y intercept so to get rid of it first you should cancel it out (subtract it from itself) and then you should alsp subtract it from the dependant variable (y) to make it even. Then your equation will look like this: y=mx sowhat you need to do is divide m by m to leave x alone and also divide y by m and that would be your result y=x. (Look at the example for further information).
How to find variables
Y: solving the equation

B & M: Suppose you have those two points on the line. To find the slope (m) you would first have to put the numbers like in a fraction: the y's on top and the x's on the bottom and subtract the first coordinate for y from the second coordinate (7-5) and then do the same to the x (3-2). After you subtract, the answer (fraction y/x) will be the your slope (m= 2). Then to find the y intercept (b) you would have to use only one of the sets of coordinates (It may be any). The first step would be to set the equation. Imagine you chose the first coordinates (2,5) then you would set the equation like this: 5= 2 (2) +b (y=mx+b) you would set up the y in place of y and the x in place of x and then you would just put the slope in m. Then you
would have to simplify the equation (5=4+b). After you have
done this the first step is to cancel out the 4 so you would
subtract 4-4=0 and then do the same thing to 5
(5-4=1) and your answer would be 1=b.
When does it make sense to choose a linear function to a model set of data?
Thinking with mathematical models
Tamara Canales
Math 4b

When it is linear because you don't need to put a model to set the data if it is linear because it is already a straight line.
You are given a discription of the variables in words
Example: To find the y-intercept (b) it willthe $50 because it is the fixed fee which it the amount paid that doesn't change with the time the work takes. So if it takes 0 hours you would still have to pay 50 ds extras, so it is your y-int.
Then to find your indeoendant variable (m) it will be the $50 per hour because it will be the slope which it is multiplied by the x (in this case the x will be the
number of hours. Once you get those
variables: "m" and "x" and you could
build your equation.
You are given a table of values for the variables
Example: First you need to see how much it advances in the graph from one variable to another in both sides like it is shown in the example. Then put the digits of the number it advanced y over x (y/x) and that would be your slope (remember to simplify) (look at the example for better explanation). Then to find the y intercept (b) you would have to use only one of the sets of coordinates (It may be any). The first step would be to set the equation. Imagine you chose (6,2) to be the your coordinates then you would set the equation like this: 2= 1/2 (6)+b (y=mx+b) you would set up the y in place of y and the x in place of x and then you would just put the slope in m. Then you would have to simplify the equation (2=3+b). After you have done this the first step is to cancel out the 3 so you would subtract 3-3=0 and then subtract the number you have cancelled to y (2-3= -1) and your answer would be -1=b.
You are given a graph of sample data points
Example: In a graph to find the y intercept you should look at the y axis and see which point is at 0. Then to find the slope you should look at two points on the graph and and see how much it rises and runs (look at example for further information). And then put the rise over the run in a fraction and that
would be your slope (m).
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