Use the points $(-2,4)$ and $(4,-2)$ in the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$. Be careful with negatives in the numerator and denominator.

Once you know the slope $m$, plug it and one of the points into $y=mx+b$ to solve for $b$, the $y$-intercept.

After you know both $m$ and $b$, write the equation in the form $y=mx+b$ and choose the option that has the same $m$ and $b$. You can also quickly check by plugging $x=-2$ and $x=4$ into your candidate equation to see if it gives the correct $y$-values.

Type (-2,4) and (4,-2) into Desmos in separate lines. Desmos will show these as two points on the coordinate plane.

Enter each option as a function on its own line: y = x + 2, y = -2x + 1, y = x - 2, and y = -x + 2. Each one will appear as a different line.

Zoom or pan if needed so both points are visible. Look for the line that passes exactly through both plotted points $(-2,4)$ and $(4,-2)$. The equation of that line corresponds to the correct answer choice.

A linear function $g$ that passes through $(-2,4)$ and $(4,-2)$ must satisfy both conditions:

• $g(-2)=4$
• $g(4)=-2$

Also, because it is linear, its graph is a straight line, which we can write in slope-intercept form $y=mx+b$.

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

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

Now use slope-intercept form $y=mx+b$ with $m=-1$ and one of the points, for example $(-2,4)$.

Plug in $x=-2$, $y=4$, and $m=-1$:

So the line has slope $-1$ and $y$-intercept $2$.

With slope $m=-1$ and intercept $b=2$, the equation of the line is

Since $g(x)$ represents this line, $g(x)=-x+2$, which matches choice D.