Linear and other Functions

To calculate a line passing through two points, we first need to calculate the slope, m.

${\displaystyle m=\frac{\mathrm{\Delta <!--\; \Delta \; -->}y}{\mathrm{\Delta <!--\; \Delta \; -->}x}=\frac{y_2-<!--\; -\; -->y_1}{x_2-<!--\; -\; -->x_1}=\frac{8-<!--\; -\; -->2}{1-<!--\; -\; -->(-<!--\; -\; -->3)}=\frac{6}{4}=\frac{3}{2}}$

Plug it into our equation y =mx +c.

${\displaystyle y=\frac{3}{2}x+b}$

To solve for b, we can plug in one of the points we were given. let's use (−3,2).

${\displaystyle 2=\frac{3}{2}(-<!--\; -\; -->3)+b}$

${\displaystyle 2=\frac{-<!--\; -\; -->9}{2}+b}$

${\displaystyle 2+\frac{9}{2}=b}$

${\displaystyle \frac{13}{2}=b}$

Now that we have solved for b, So the answer is C.