Once you know how many people are added per car (the slope), write an equation in the form $p = mc + b$ and plug in one table row to solve for $b$.

After you find an equation for $p$ in terms of $c$, move all terms to one side so it looks like the choices, with $55c$ and $p$ on the same side and a constant on the other.

In Desmos, evaluate the expression $55c - p$ using the table rows:

• Type 55*3 - 174 and note the result.
• Type 55*5 - 284 and 55*10 - 559 and see if these give the same value as the first one. If all three match, then the correct equation must have the left side $55c - p$ and equal that common constant.

Now compare that constant from step 1 to the constants in the choices with $55c - p$ on the left (options A and D). Choose the option whose right-hand side matches the value Desmos gave you.

Enter the $c$ values in a table column x1 and the corresponding $p$ values in y1. Then type y1 ~ m x1 + b to have Desmos find the line that fits the points. The values of $m$ and $b$ shown by Desmos give you the slope and intercept in $p = mc + b$; then rearrange this equation into the same form as the answer choices and select the matching one.

Use any two rows to find how much the maximum number of people changes per additional car.

From 3 cars to 5 cars:

• Change in $c$: $5 - 3 = 2$
• Change in $p$: $284 - 174 = 110$

So the rate of change is

This means each extra car adds 55 people.

Use the form $p = mc + b$, where $m$ is the slope and $b$ is the vertical intercept.

You found $m = 55$, so start with

Now plug in any point from the table, for example $(c, p) = (3, 174)$:

Compute $55(3) = 165$, so

Thus the relationship in slope-intercept form is

The answer choices are all written with everything on one side of the equation, like $55c - p = \text{constant}$ or $55p - c = \text{constant}$.

Start from the equation you found:

Move all terms to one side. Subtract $p$ from both sides:

Now subtract 9 from both sides:

Rewrite this as

which matches answer choice D.