Question

a car is traveling on a highway. the distance (in miles) from its destination and the time (in hours) is given by the equation ( d = 420 - 65t ). what is the slope of the line represented by the equation? what is the practical meaning of the slope?
a. ( m = 420 ); the total distance is 420 miles.
b. ( m = 65 ); the car is traveling 65 miles per hour.
c. ( m = -65 ); the car is traveling 65 miles per hour.
d. ( m = -420 ); the total distance is 355 miles.

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

The equation of a line is typically in the form \( y = mx + b \), where \( m \) is the slope. Rewriting the given equation \( d = 420 - 65t \) in slope - intercept form (\( d=-65t + 420\)), we can see that the slope \( m=-65\). The slope represents the rate of change of the distance from the destination with respect to time. A negative slope here means that as time (\( t \)) increases (in hours), the distance (\( d \)) from the destination decreases. The magnitude of the slope, 65, represents the speed at which the car is approaching the destination, or in other words, the car is traveling at 65 miles per hour.

Now let's analyze each option:

• Option A: The slope is not 420. 420 is the initial distance (when \( t = 0\)), so this option is incorrect.
• Option B: The slope is not 65 (it's - 65), so this option is incorrect.
• Option C: The slope \( m=-65\) and the practical meaning (the car is traveling 65 miles per hour towards the destination) is correct.
• Option D: The slope is not - 420, and the description about the total distance is also incorrect.

Answer:

C. \( m = - 65 \); The car is traveling 65 miles per hour.