Answer
$f(x)=2x+16$
Work Step by Step
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, then the equation of the line passing through $
(-9,-2) \text{ and } (-3,10)
,$ is
\begin{array}{l}\require{cancel}
y-(-2)=\dfrac{-2-10}{-9-(-3)}(x-(-9))
\\\\
y+2=\dfrac{-2-10}{-9+3}(x+9)
\\\\
y+2=\dfrac{-12}{-6}(x+9)
\\\\
y+2=2(x+9)
\\\\
y+2=2x+18
\\\\
y=2x+18-2
\\\\
y=2x+16
.\end{array}
In function notation, this is equivalent to $
f(x)=2x+16
.$