Use $m = \dfrac{\Delta y}{\Delta x}$ with any two points from the table to find the slope of the line.

Once you know the slope $m$, write the equation as $g(x) = mx + b$ and plug in one $(x, g(x))$ pair from the table to solve for $b$.

In Desmos, add a table and enter the three points from the problem: $(-3,11)$, $(-1,7)$, and $(1,3)$. You should see these three points plotted on the graph.

In new lines, type each option as an equation in $y$ (for example, y = 2x + 5, y = -2x - 5, etc.). Desmos will draw four straight lines, one for each choice.

Look for the line that passes exactly through all three plotted points from the table. The equation of that line is the correct choice.

Look at how $g(x)$ changes when $x$ increases:

• From $x=-3$ to $x=-1$, $x$ increases by 2 and $g(x)$ goes from 11 to 7, which is a change of $7-11=-4$.
• From $x=-1$ to $x=1$, $x$ increases by 2 and $g(x)$ goes from 7 to 3, which is a change of $3-7=-4$.

So for every increase of 2 in $x$, $g(x)$ decreases by 4.

The slope $m$ of a linear function is

Using the changes from the table:

So the slope of $g(x)$ is $-2$, meaning the equation has the form $g(x) = -2x + b$ for some constant $b$.

Use any point from the table, for example $(1,3)$, and substitute into $g(x) = -2x + b$:

• Plug in $x=1$ and $g(x)=3$:

• Simplify: $3 = -2 + b$, so $b = 5$.

Thus the equation is $g(x) = -2x + 5$, which corresponds to choice C.