Once you know the slope $m$, write the equation as $y = mx + b$. Then you only need to find the value of $b$.

Take one of the given points and substitute its $x$ and $y$ values into $y = mx + b$ to solve for $b$. Then compare your final equation with the answer choices.

In Desmos, type (-4,3) and (2,-9) on separate lines so you can see the two points that line $w$ must pass through.

On new lines in Desmos, enter each option exactly as written: y = 2x - 5, y = -2x + 5, y = 2x + 5, and y = -2x - 5. You will see four different lines on the graph.

Look at the graphs and check which of the four lines passes exactly through both plotted points $(-4,3)$ and $(2,-9)$. The equation of that line is the correct choice for line $w$.

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

Let $(-4,3)$ be $(x_1,y_1)$ and $(2,-9)$ be $(x_2,y_2)$.

Then

So the slope of line $w$ is $-2$.

A line with slope $m$ can be written in slope-intercept form as $y = mx + b$, where $b$ is the $y$-intercept.

We found $m = -2$, so line $w$ must have an equation of the form

Among the answer choices, only the ones with slope $-2$ (the coefficient of $x$ is $-2$) can be correct.

Substitute one of the points, say $(-4,3)$, into $y = -2x + b$ to solve for $b$:

So the equation of line $w$ is $y = -2x - 5$, which corresponds to choice D.