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:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
We are given the equation $d=420 - 65t$. We can rewrite this equation in the form $d=- 65t + 420$.

Step2: Identify the slope

Comparing $d=-65t + 420$ with $y = mx + b$, we can see that the slope $m=-65$.

Step3: Interpret the slope

The variable $d$ represents the distance from the destination and $t$ represents time. The slope $m=-65$ means that for each hour ($t$ increases by 1), the distance from the destination ($d$) decreases by 65 miles. This is equivalent to saying that the car is traveling at a speed of 65 miles per hour (since the distance to the destination is decreasing as the car moves towards it).

Answer:

C. $m = - 65$; The car is traveling 65 miles per hour.