Check how $f(x)$ changes as $x$ increases by 1 each time. Is the change the same every time? That tells you the slope.

Once you know the slope and one point from the table, plug them into $y = mx + b$ to find $b$. Then use that equation to find the value of $x$ when $y=0$.

Create a table and enter the $x$-values $-11$, $-10$, $-9$, $-8$ in the first column and the corresponding $f(x)$ values $21$, $18$, $15$, $12$ in the second column. You should see four points plotted.

In a new expression line, type y1 ~ m x1 + b. Desmos will show values for $m$ and $b$ that give the best-fitting line through your four points (these should match the exact linear pattern in the table).

In another expression line, type y = m x + b using the $m$ and $b$ values from the regression. This will graph the full line that matches the table.

Look for where this line crosses the $x$-axis (where $y=0$). Tap or click that intersection point and read off the $x$-coordinate; that $x$-value gives you the correct answer choice.

The $x$-intercept is the point where the graph crosses the $x$-axis. On the $x$-axis, the $y$-value is $0$.

So we are looking for the value of $x$ such that $f(x)=0$, and the answer will be a point of the form $(x,0)$.

Look at how $f(x)$ changes when $x$ increases by 1:

• From $x=-11$ to $x=-10$: $f(x)$ goes from $21$ to $18$ (change $-3$)
• From $x=-10$ to $x=-9$: $f(x)$ goes from $18$ to $15$ (change $-3$)
• From $x=-9$ to $x=-8$: $f(x)$ goes from $15$ to $12$ (change $-3$)

Each time $x$ increases by $1$, $f(x)$ decreases by $3$, so the slope is

Use the slope $m=-3$ and any point from the table, for example $(-11,21)$.

Use the slope-intercept form $y=mx+b$:

Substitute $x=-11$, $y=21$, and $m=-3$:

Compute $-3(-11)$:

Solve for $b$:

So the equation of the line is

At the $x$-intercept, $y=0$. Use the equation $y=-3x-12$ and set $y$ to $0$:

Add $12$ to both sides:

Divide both sides by $-3$:

So the $x$-intercept is the point where $x=-4$ and $y=0$, which is $(-4,0)$.