Apply $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ with $(-4,3)$ and $(8,-9)$ to find the slope $m$ of the line.

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

After finding both $m$ and $b$, write the full equation and see which answer choice has the same $m$ and $b$ values.

Type (-4,3) and (8,-9) into Desmos on separate lines so you can see the two points the line must pass through.

On new lines, enter each option exactly as written: y=-x+1, y=-x-6, y=-x, and y=-x-1. Four lines will appear on the graph.

Look for the one line that goes exactly through both plotted points $(-4,3)$ and $(8,-9)$. The equation of that line is the correct answer choice.

Use the slope formula with the two points $(-4,3)$ and $(8,-9)$:

Compute the numerator and denominator:

• Numerator: $-9 - 3 = -12$
• Denominator: $8 - (-4) = 8 + 4 = 12$

So the slope is

Slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

We found $m = -1$, so the line has the form

Now we just need to find the value of $b$.

Use either of the given points. Let's use $(-4,3)$ and substitute $x=-4$, $y=3$ into $y=-x+b$:

Simplify:

• $-(-4) = 4$, so

Solve for $b$:

With $m=-1$ and $b=-1$, the equation of the line is

Among the answer choices, this corresponds to choice D) $y=-x-1$. This equation will make both points $(-4,3)$ and $(8,-9)$ true when you substitute them in.