Question

Escatter plot shows the distance a car drives and the time it takes to get to the destination for many trips.

travel time (min)
y₁
80
70
60
50
40
30
20
10 t
10 20 30 40 50 60 70 80 X
distance (mi)
POSSIBLE POIN
A line that models the data is given by the equation y = 0.93x + 4.15, where y represents the travel time in minutes, and x represents the
distance travel in miles.
1. The slope of the line is 0.93. What does this mean in this situation? Is it realistic?
2. The y-intercept is (0, 4.15). What does this mean in this situation? Is it realistic?

Answer 1

The slope of 0.93 in the equation represents the time in minutes it takes to travel each additional mile, which is a realistic scenario assuming near-constant speed. The y-intercept of 4.15 represents the initial time delay before the car starts moving, which can be realistic depending on usual pre-travel activities or delays.

Step-by-step explanation:

The slope of the line in the equation y = 0.93x + 4.15 represents the rate of change between distance and time. In this context, it means that for each additional mile driven, the travel time increases by approximately 0.93 minutes. This is a realistic scenario as it suggests that the car is traveling at a near-constant speed.

The y-intercept (0, 4.15) represents the travel time when the distance traveled is zero. In real-life terms, this could be interpreted as the initial time spent before the car begins to move, such as starting the engine or waiting at a stoplight. While a y-intercept of over four minutes may seem high, depending on the situation, it could be considered realistic if there is usually a consistent delay before starting each trip.