Question 97·Medium·Algebra

Pick two points that lie exactly on the line (for example, a labeled point and the intercept) and compute $\frac{\Delta p}{\Delta t}$.

Once you have slope $m$ and intercept $b$, compare to the answer choices written in the form $p = mt + b$.

In Desmos, enter the points (0,30) and (5,80).

Type y=mx+b to create sliders $m$ and $b$. (Here, treat $x$ as $t$ and $y$ as $p$.)

Adjust $b$ so the line goes through $(0,30)$, then adjust $m$ so it also goes through $(5,80)$.

Compare the resulting values of $m$ and $b$ to the four options and select the one with the same slope and intercept.

The line crosses the vertical axis at $(0,30)$. That means when $t=0$, $p=30$, so the $p$-intercept is $30$.

Another clear point on the line is $(5,80)$.

Compute the slope:

A line with slope $10$ and $p$-intercept $30$ has the form $p = 10t + 30$.

So the correct choice is $p = 10t + 30$.