Question

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

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

(b) Draw the graph of the equation in part (a).

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

Short answer

(a) The equation of the distance function is\(d = 48\,t\).

(b) The graph of \(d = 48\,t\) .

(c) The slope represents the car’s speed in\({\rm{miles/h}}\).

Step-by-step solution

Given data

Jason leaves Detroit at 2:00 PM and drives at a constant speed west along I-96,

and passes Ann Arbour, 40 mi from Detroit, at 2:50 PM.

(a) Determine the distance traveling in terms of the time elapsed

Use the slope formula to find the value of\(m\).

The slope formula is given as shown below:

\(m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\)

So, the slope is calculated as follows:

\(\begin{array}{c}m = \frac{{40 - 0}}{{\left( {\frac{5}{6} - 0} \right)}}\\\;\;\; = \frac{{40}}{{\frac{5}{6}}}\\\;\;\; = \frac{{240}}{5}\\ = 48\;{\rm{miles/}}{{\rm{h}}^{\rm{2}}}\end{array}\)

Therefore, the equation of the distance function is\(d = 48\,t\) .\(\)\(\)

(b) Draw the graph of the equation

The graph of\(d = 48\,t\):

(c) Find the slope of this line

From part (a), it is clear that the slope of the line is\(m = 48\).

This represents the car’s speed in\({\rm{miles/h}}\).