Once you have the two points, use the slope formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$. Be careful with the negatives when subtracting.

After you find the slope $m$, write $y = mx + b$ and plug in one of the given points to solve for $b$.

When you have an equation in the form $y = mx + b$, match both the slope and the $y$-intercept to the given answer choices.

In one expression line, type (-2, 7). In another line, type (4, -5). You should see the two points plotted on the coordinate plane.

In separate expression lines, type each option exactly: y = -2x - 3, y = 2x + 3, y = 2x - 3, and y = -2x + 3. Four lines will appear.

Look at which of the four lines passes through both plotted points (-2, 7) and (4, -5). The equation of that line matches the function f and is the correct choice.

A statement like $f(a)=b$ means that when $x=a$, $y=b$ on the graph of the function.

So the information

• $f(-2)=7$ means the point $(-2,7)$ is on the line.
• $f(4)=-5$ means the point $(4,-5)$ is on the line.

We are looking for a line that passes through both $(-2,7)$ and $(4,-5)$.

Use the slope formula with points $(-2,7)$ and $(4,-5)$:

So the slope of the line must be $-2$.

A line in slope-intercept form is $y = mx + b$.

We already found $m=-2$, so the equation must look like $y = -2x + b$.

Now plug in one of the points, for example $(-2,7)$:

Compute $-2(-2)=4$, so:

Therefore, the $y$-intercept is $3$.

With slope $-2$ and intercept $3$, the line’s equation is

This matches answer choice D.