As $x$ increases from $-2$ to $4$, does $y$ increase or decrease? Should the slope be positive or negative based on how the points move?

Once you know the slope $m$, write the equation as $y = mx + b$ and plug in one of the points to solve for $b$.

After you find an equation, plug in both $(-2,-3)$ and $(4,0)$ to make sure they satisfy it. Only one answer choice will work for both points.

In Desmos, type (-2, -3) and (4, 0) on separate lines to plot the two points. You should see them appear on the graph.

Type y = -1/2 x - 2 into Desmos. Check whether this line goes exactly through both plotted points $(-2,-3)$ and $(4,0)$. If it misses either point, this choice is not correct.

Type y = 1/2 x + 2. Again, check whether the line passes through both plotted points. If it does not pass through both, eliminate this option.

Type y = 1/2 x - 2. See whether this line goes through both $(-2,-3)$ and $(4,0)$. If it does, note that this equation is a candidate for the correct answer.

Type y = -1/2 x + 2. Check whether this line passes through both given points. After testing all four, identify which line contains both points; that equation is the correct choice.

Use the slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$:

Let $(x_1,y_1)=(-2,-3)$ and $(x_2,y_2)=(4,0)$:

So the slope $m$ of the line is positive and equals $\tfrac12$. This immediately tells you the correct equation must have a positive slope.

A line with slope $m$ can be written in slope-intercept form as

You already found $m = \tfrac12$, so substitute that into the equation:

Now you just need to find the value of $b$, the $y$-intercept.

The line passes through both given points, so each point must satisfy $y = \tfrac12 x + b$.

Use the point $(4,0)$ and substitute $x=4$ and $y=0$:

Solve for $b$:

So the $y$-intercept of the line is $-2$.

Now substitute $b=-2$ back into the equation $y = \tfrac12 x + b$:

This matches answer choice C) $y = \tfrac12 x - 2$, which is the equation of the line through $(-2,-3)$ and $(4,0)$.