Answer
$(A) -5$.
Work Step by Step
The given points are
$(x_1,y_1)=(2,-1)$
and $(x_2,y_2)=(3,1)$
Slope:
$m=\frac{y_2-y_1}{x_2-x_1}$
Substitute all values.
$m=\frac{1-(-1)}{3-2}$
Simplify.
$m=\frac{1+1}{1}$
$m=2$
The slope intercept form of the line is
$\Rightarrow y=mx+c$
Where $c$ is the $y-$ intercept.
Substitute $(x,y)=(2,-1)$ and slope $m=2$ into the line and solve for $c$.
$\Rightarrow -1=(2)(2)+c$
Simplify.
$\Rightarrow -1=4+c$
$\Rightarrow -1-4=c$
$\Rightarrow -5=c$
Hence, the correct option is $(A) -5$.
