Once you know the slope $m$, think about what $f(0)$ tells you in the equation $f(x)=mx+b$. Which part of the equation is the value when $x=0$?

After finding both the slope and the value of $f(0)$, write $f(x)$ in the form $mx+b$. Then look for the choice with that same $m$ and $b$.

In Desmos, add a table and enter the $x$ values 0, 1, 2 in the first column, and the corresponding $f(x)$ values 29, 32, 35 in the second column. These points represent the function from the problem.

In separate lines, type each option: f(x)=29x+32, f(x)=35x+29, f(x)=32x+35, and f(x)=3x+29. Desmos will draw four lines.

Look at which line passes exactly through all three table points you entered (0,29), (1,32), and (2,35). The equation for that line is the correct choice.

For a linear function, the slope is the change in $f(x)$ divided by the change in $x$.

From $x=0$ to $x=1$:

• $f(x)$ changes from 29 to 32, so the change in $f(x)$ is $32-29=3$.
• $x$ changes from 0 to 1, so the change in $x$ is $1-0=1$.

So the slope is $m = \dfrac{3}{1} = 3$. This same change (from 32 to 35) occurs from $x=1$ to $x=2$, confirming the slope is constant and equal to 3.

A linear function in slope-intercept form is $f(x)=mx+b$, where $b$ is the $y$-intercept, the value when $x=0$.

From the table, when $x=0$, $f(0)=29$. So $b=29$ in the equation $f(x)=mx+b$.

We have:

• Slope $m=3$
• Intercept $b=29$

Substitute these into $f(x)=mx+b$ to get the equation of the function:

Comparing with the answer choices, this matches choice D.