Question

Write a linear Write a linear function f with f(−9)=10 and f(−1)=−2.function f with f(−9)=10 and f(−1)=−2.

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have

f(-9) = 10 → (-9, 10)

f(-1) = -2 → (-1, -2)

Substitute:

$m=\dfrac{-2-10}{-1-(-9)}=\dfrac{-12}{8}=-\dfrac{3}{2}=-1.5\\\\y-10=-1.5(x-(-9))\\\\y-10=-1.5(x+9)\qquad|\text{use distributive property}\\\\y-10=-1.5x-13.5\qquad|+10\\\\y=-1.5x-3.5$

Answer: f(x) = -1.5x - 3.5