Answer
$f(x)=-3x-2$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is $m$, then the point-slope form of the line is.
$\Rightarrow y−y_1=m(x−x_1)$
We are given both a point and the slope:
$\Rightarrow (x_1,y_1)=(1,-5)$
and slope $m=-3$.
Substitute all values into the equation.
$\Rightarrow y−(-5)=-3(x−1)$
Use the distributive property.
$\Rightarrow y+5=-3x+3$
Substract $5$ from both sides.
$\Rightarrow y+5-5=-3x+3-5$
Simplify.
$\Rightarrow y=-3x-2$
Replace $y$ by $f(x)$.
$\Rightarrow f(x)=-3x-2$.
