Use the slope formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ with the points $(-2,-7)$ and $(4,5)$. Be careful with the negative signs.

Once you know the slope, either (1) plug one point into $y=mx+b$ to solve for $b$, or (2) test the answer choices by substituting $x=-2$ and checking which function gives $-7$.

In Desmos, type (-2,-7) on one line and (4,5) on another. Desmos will plot these two points on the coordinate plane.

On separate lines, enter each option as a function of $x$, for example:

• y = 2x + 3
• y = -2x - 3
• y = 2x - 3
• y = -2x + 3 This will draw four different lines.

Look at the graph and see which line passes exactly through both plotted points $(-2,-7)$ and $(4,5)$. The equation of that line is the correct choice.

A linear function $g$ is the same as a straight line. The question tells you two points on this line:

• When $x=-2$, $g(-2)=-7$ → the point $(-2,-7)$
• When $x=4$, $g(4)=5$ → the point $(4,5)$

We need the equation of the line that goes through these two points.

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

So the slope of the line is $m=2$.

Use slope-intercept form $y=mx+b$ with $m=2$ and one of the points, say $(-2,-7)$.

Substitute $x=-2$, $y=-7$, and $m=2$ into $y=mx+b$:

Add $4$ to both sides:

So $b=-3$, and the equation is $g(x)=2x-3$, which matches choice C.