Write a linear function f with the values f(−2)=3 and f(5)=7.

Question

I do not understand any of this. Please help me.

Answer 1

A linear function takes the form f(x)=mx+a, where m is the slope and constant a the y intercept.

f(-2)=3 and f(5)=7. The slope is (f(5)-f(-2))/(5-(-2))=(7-3)/(5+2)=4/7=m.

We can find a in two different ways.

1. Plug in one of the points, for example, (-2,3): f(-2)=(4/7)(-2)+a, 3=(-8/7)+a, a=3+(8/7)=29/7. f(x)=4x/7+29/7 which can be written f(x)=(1/7)(4x+29).
2. Using (-2,3) again: f(x)-3=(4/7)(x-(-2))=(4/7)(x+2), f(x)=(4/7)(x+2)+3=4x/7+8/7+3=4x/7+29/7 or f(x)=(1/7)(4x+29).