Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 14

Jason leaves Detroit at 2:00pm and drives at a constant speed west along I-96. He passes Ann Arbor, 40 mi from Detroit, at 2:50pm.


(a.) Express the distance traveled in terms of the time elapsed.



$
\begin{equation}
\begin{aligned}
\text{Velocity} &= \frac{\text { distance }}{\text { time }}; \text{ but velocity is constant, so let velocity} = a\\
\text{distance} &= at, \text{ where } t = \text{time elapsed}\\
\text{when } t &= 50 \text{ minutes}, D = 40 \text{ miles}, \text{ so } a = \frac{4}{5}
\end{aligned}
\end{equation}
$


$\boxed{D (t) = \frac{4}{5}t}$



(b.) Graph the equation in part (a.)









(c.) Find the slope of this line. What does it represent?



$\boxed{\text{The slope is }\frac{4}{5},\text{ it represents the equivalent distance in miles with time in minutes.}}$