Expert: Sherry Wallin - 9/22/2009

Question
I am trying to figure out how to express the rules for two different function tables.  In the first, x = 2, 3, 4, 5 and y = 2, 5, 8, 11.  I can see x goes up by 1 and y goes up by x + 2 more each time (x + 0; x+2; x+4; x+6).

In the second x = 3, 6, 9, 12, and y = 13, 28, 43 and 58.  x goes up by 3 and the difference between x and y goes up by 12.

Answer
RDC~
    Here is a detailed solution to the first problem. Write the function as a set of ordered pairs and then use any two to find the slope and then use one of the points and the slope in the point slope form of the equation of a line and then transform (change) that equation into the slope intercept form of the equation of a line which just means solve for y.

m = (5-2)/(3-2) = 3/1
using the point (2,2) and writing the point slope form: y-2 = 3(x-2)-> y = 3x - 6 + 2 -> y = 3x -4
You can check that this is the 'right' function by checking:
f(2)=2
f(3)=5
f(4)=8
f(5)=11

As for the 2nd problem I am not sure how you are getting that as x goes up by 3 y goes up by 12 because if this were true then the 2nd ordered pair would be (6,25). I think you meant to say that when x goes up by 3 that y goes up by 15 (which it does). what does it mean when you examine the behavior of y based on your observation of x? Remember that y depends on x and that the definition of slope is the change in y over the change in x. So if the change in y is 15 when the change in x is 3 you have slope = 15/3 = 5. Now complete the problem as I did for number 1.

Math Prof