Once you know the slope $m$, write $f(x)$ in the form $f(x) = mx + b$ and plug in the coordinates of one table point to solve for $b$.

After you know $f(x)$, replace $f(x)$ in $h(x) = f(x) - 13$ with your expression for $f(x)$, then simplify.

From the table, we found that the slope of $f$ is $5$ and that $f(-4) = 0$, which leads to $f(x) = 5x + 20$. In Desmos, type f(x) = 5x + 20 to graph this function.

In a new line in Desmos, type h(x) = f(x) - 13. Desmos will automatically show the graph and expression for $h(x)$ based on this definition.

Use the Desmos input line or table feature to evaluate $h(x)$ at $x = -4$, $x = -19/5$, and $x = -18/5$. Then compare the pattern of outputs to what each answer choice would produce (all choices are lines with slope 5 but different intercepts) and see which one matches the $h(x)$ values shown by Desmos.

Because $f$ is linear, its graph is a straight line with a constant slope.

Use any two points from the table. The second and third points are convenient:

• Point 1: $\left(-\dfrac{19}{5}, 1\right)$
• Point 2: $\left(-\dfrac{18}{5}, 2\right)$

Compute the slope $m$:

So the slope of $f$ is $5$. That means $f(x)$ has the form $f(x) = 5x + b$ for some constant $b$.

Now use any point from the table to solve for $b$ in $f(x) = 5x + b$.

Use the point $(-4, 0)$:

So

Thus, the linear function is

We are told that $h(x) = f(x) - 13$.

Now substitute the expression we found for $f(x)$:

This gives $h(x)$ as a linear expression in $x$ that you can simplify.

Simplify the expression from the previous step:

So the equation that defines $h$ is

which corresponds to choice B.