Answer
$ f(x)=2x+1$.
Work Step by Step
The given points are
$(-2,-3)$ and $(2,5)$.
We determine the slope of the line:
$\Rightarrow m=\frac{change \; in \; y-\;coordinates}{change \; in \; x-\;coordinates}$
$\Rightarrow m=\frac{5-(-3)}{2-(-2)}$
Simplify.
$\Rightarrow m=\frac{5+3}{2+2}$
$\Rightarrow m=\frac{8}{4}$
$\Rightarrow m=2$
The point-slope form of the line passing through the point $(x_1,y_1)$ and having slope $m$ is.
$\Rightarrow y-y_1=m(x-x_1)$
Let the point is $(x_1,y_1)=(2,5)$.
Substitute all values into the point-slope equation.
$\Rightarrow y-5=2(x-2)$
Simplify.
$\Rightarrow y-5=2x-4$
Add $5$ to both sides.
$\Rightarrow y-5+5=2x-4+5$
Simplify.
$\Rightarrow y=2x+1$
Let $y=f(x)$.
$\Rightarrow f(x)=2x+1$.
