Chapter 4 - Writing Linear Functions - 4.2 - Writing Equations in Point-Slope Form - Exercises - Page 185: 22

$ f(x)=x+2$

$f(5)=7$ can be written as $(5,7)$ and $f(-2)=0$ as $(-2,0)$ Slope $m=\frac{0-7}{-2-5}=\frac{-7}{-7}=1$ Point-slope form is $y-y_{1}=m(x-x_{1})$ Using the values of slope $m$ and point $(-2,0)$, we get $y-0=1(x-(-2))$ $\implies y=x+2$ A linear function is $ f(x)=x+2$