Once you have the two points, use $m = \dfrac{P_2 - P_1}{u_2 - u_1}$ to find the slope of the linear profit function.

Use point-slope form, $P - P_1 = m(u - u_1)$, with the slope you found and one of the points (for example, the break-even point). Then simplify to get $P$ in terms of $u$.

After you get an equation, plug in $u = 150$ and $u = 300$. It should give $P = 0$ at 150 units and $P = 3300$ at 300 units.

In Desmos, treat $u$ as $x$ and $P$ as $y$. Type each option on its own line, replacing $u$ with $x$ and $P$ with $y$ (for example, y = -22x - 3300, y = 3300x - 22, etc.).

On new lines in Desmos, type the points (150,0) and (300,3300) so they appear on the graph. These represent the break-even point and the $3300 profit point.

Look at the graph and identify which one of the four lines passes exactly through both points $(150,0)$ and $(300,3300)$. The equation of that line in the left panel is the correct model for $P$ as a function of $u$.

The profit $P$ is a linear function of units sold $u$, so each situation is a point $(u,P)$ on a line.

• "Breaks even" means profit is $0 dollars.
  • So when 150 units are sold, the point is $(150,0)$.
• The business earns $3300 when 300 units are sold.
  • So the second point is $(300,3300)$.

For a linear function, the slope $m$ is

Use the points $(150,0)$ and $(300,3300)$:

So the profit increases by $22 per extra unit sold.

Use point-slope form with slope $m=22$ and the point $(150,0)$:

This is an equation for $P$ as a function of $u$, but we can rewrite it in slope-intercept form to compare to the answer choices.

Distribute the 22 in the equation from the previous step:

So the function is $P = 22u - 3300$, which corresponds to choice D.