Decide which point will be $(x_1,y_1)$ and which will be $(x_2,y_2)$, and keep that order the same in both the numerator and denominator.

Find $y_2 - y_1$ and $x_2 - x_1$, form the fraction, and then simplify it by dividing the numerator and denominator by their greatest common factor.

In a Desmos expression line, type (6-3)/(4-(-2)) and press Enter. The numerical value Desmos gives you is the slope between the points $(-2,3)$ and $(4,6)$; match this value to the closest fraction choice.

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

This is "change in $y$ over change in $x$" (rise over run).

Let $(-2,3)$ be $(x_1,y_1)$ and $(4,6)$ be $(x_2,y_2)$.

• Change in $y$:

• Change in $x$:

Now plug these into the slope formula:

Simplify $\frac{3}{6}$ by dividing the top and bottom by $3$:

So, the slope of the line is $\dfrac{1}{2}$, which corresponds to choice A.