Once you have the two points, use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ to find the slope of the line.

Put the line in the form $y=mx+b$ using the slope you found, then plug in one of the points to solve for $b$.

Once you have the slope and intercept, compare your equation to each answer choice and also make sure it gives the correct $y$-values for $x=-2$ and $x=6$. Only one choice will work for both.

In Desmos, type each option as a separate equation: y=-x+5, y=x+5, y=-x-5, and y=x-5. You will see four lines on the graph.

Add a table and enter $x=-2$ and $x=6$ in the first column, then enter the corresponding $y$-values $7$ and $-1$ in the second column to create the points $(-2,7)$ and $(6,-1)$ on the graph.

Look at which line passes exactly through both plotted points $(-2,7)$ and $(6,-1)$. The equation of that line is the correct choice.

A linear function $f$ with values $f(-2)=7$ and $f(6)=-1$ means its graph passes through two points:

• When $x=-2$, $y=7$, so one point is $(-2,7)$.
• When $x=6$, $y=-1$, so the other point is $(6,-1)$.

We are looking for the equation of the line that goes through these two points.

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

Let $(x_1,y_1)=(-2,7)$ and $(x_2,y_2)=(6,-1)$:

So the slope of the line is $m=-1$.

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

We already know $m=-1$, so the equation has the form

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

• Substitute $x=-2$ and $y=7$ into $y=-x+b$ and solve for $b$.

Substitute $(-2,7)$ into $y=-x+b$:

So the equation of the line is

In function notation, this is $f(x) = -x + 5$, which matches answer choice A.