Expert: Sherry Wallin - 6/11/2009

Question
Thank you so much for help earlier, I was on the right track but made a silly error.
I tried your method to another problem, I tried add,subtract,divide,multiply and exponents.  I think it's a combination. (1,5) (5,1) (9,-3) Where do you begin? Please help.

Answer
Ok Sabrina~
    This is just one of probably many ways to figure this problem out but its the way that makes the most and simplest sense to me to show you.
    Since you really have 3 pairs of points you only 2 points to determine a line and you only need 2 point to find the slope, correct?
Once you find the slope, you can actually use the point-slope equation to find the equation which when solve for y is a function of x. This is how:

[5-1]/[1-5] =4/-4 = -1 this is the slope using (1,5)and (5,1)
y -1 = -1(x - 5)
y -1 = -x + 5
y = -x + 6

using the slope -1 and (1,5)

Since y = f(x) and y = -x + 6 then f(x) = -x + 6

Now you calculate all your x's in this function
f(1) =
f(5) =
f(9) =

It works for all 3 points!

Notice this worked because I made the assumption that the function was a linear function (graphed as a line). If the function was not linear this wouldn't have worked. Since it is linear we get two things free of charge. The slope is the same for all point on the line and the constant in y = mx + b is the same because it is the same line. Since it seems like you are working with elementary to intermediate algebra it made sense to me to try a linear function. Is this clear?

Math Prof