Answer
$f(x)=x-5$.
Work Step by Step
Rewrite as shown below.
$f(10)=5$ as $(10,5)$
and $f(2)=-3$ as $(2,-3)$
Let $(x_1,y_1)=(10,5)$ and $(x_2,y_2)=(2,-3)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{-3-5}{2-10}$
Simplify.
$\Rightarrow m =\frac{-8}{-8}$
$\Rightarrow m =1$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-(5)=1(x-10)$
Simplify.
$\Rightarrow y-5=x-10$
Add $5$ to each side.
$\Rightarrow y-5+5=x-10+5$
Simplify.
$\Rightarrow y=x-5$
Hence, the function is $f(x)=x-5$.
