Answer
The linear function is $f(x)=5x+13$.
Work Step by Step
Rewrite as shown below.
$f(-3)=-2$ as $(-3,-2)$
and $f(-2)=3$ as $(-2,3)$
Let $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(-2,3)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{3-(-2)}{-2-(-3)}$
Simplify.
$\Rightarrow m =\frac{3+2}{-2+3}$
$\Rightarrow m =\frac{5}{1}$
$\Rightarrow m =5$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-(-2)=5(x-(-3))$
Simplify.
$\Rightarrow y+2=5(x+3)$
$\Rightarrow y+2=5x+15$
Subtract $2$ from each side.
$\Rightarrow y+2-2=5x+15-2$
Simplify.
$\Rightarrow y=5x+13$
Hence, the linear function is $f(x)=5x+13$.
