For the linear function f(x) =ax+b, where a and b are constants, f(-2)=7 and f(2)=1,find the values of a and b?.... Please help think you...

Answer 1

This is just a disguised system of equations function. Remember that f(x) is just a fancy way of writing y. Thus, you have two points here (-2,7) and (2,1). From there, you just create two equations and solve for what you don't know.

7 = -2a+b

1 = 2a+b

This works out nicely, as you can just add the two equations together to solve for b (since -2a and 2a add to 0).

8 = 2b

b = 4

Plug in b into either equation (we'll do the first one):

7 = -2a+4

3 = -2a

3/-2 = a

Thus, the values of a and b are -3/2 and 4 respectively.