Look at the coefficient of $x$ in each answer choice. Which choices have a slope that matches the one you found from the table?

After you know the slope, plug in the $x$- and $g(x)$-values from one table row into $y = mx + b$ to solve for $b$, the $y$-intercept.

In Desmos, add a table and enter the three points from the problem: $(-1,4)$, $(1,0)$, and $(3,-4)$ so you can see them on the coordinate plane.

Type each option as a separate line in Desmos: y = 2x - 2, y = -2x + 2, y = -1/2 x + 2, and y = 2x + 2. Make sure all four lines are visible.

Look at which line passes exactly through all three plotted points from the table. The equation of that line is the correct definition of $g(x)$.

Pick any two points from the table, for example $(-1,4)$ and $(1,0)$.

Use the slope formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$:

So the slope of $g(x)$ is $-2$.

In slope-intercept form, a linear equation looks like $y = mx + b$, where $m$ is the slope.

Check the slope (the coefficient of $x$) in each option:

• $2x-2$ has slope $2$
• $-\dfrac{1}{2}x+2$ has slope $-\dfrac{1}{2}$
• $2x+2$ has slope $2$

Only one option has slope $-2$. Keep that one; the others can be discarded.

Now use the slope $-2$ and any point from the table to find the $y$-intercept $b$.

Use the point $(1,0)$ in $y = mx + b$ with $m = -2$:

So $0 = -2 + b$, which means $b = 2$.

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

So the function is $g(x) = -2x+2$, which matches choice B.