Question

question 3 of 5
select the correct graph and equation.
tony is 360 miles away from home. he is returning back at a rate of 40 miles per hour. determine which graph and which equation represents tony’s distance from home, d, after t hours.
graphs
four graphs are shown here, with axes labeled d (distance) and t (time).
equations
d = 360t + 40
d = 360 - 40t
d = 360 + 40t
d = 40t - 360

Explanation:

Step1: Analyze the problem

Johnny starts 360 miles from home and drives back at 40 mph. So distance from home \( D \) should decrease over time \( h \), starting at 360 when \( h = 0 \). The equation should be \( D = 360 - 40h \).

Step2: Analyze the graphs

We need a graph where \( D \) starts at 360 (when \( h = 0 \)) and decreases linearly. Let's check the y - intercept (when \( h = 0 \)). The bottom - right graph has \( D = 360 \) when \( h = 0 \) and decreases (since slope is - 40, negative slope for decreasing distance). The equation \( D=360 - 40h \) matches the situation (starting distance 360, decreasing by 40 miles each hour).

Answer:

Graph: The bottom - right graph (with \( D \) starting at 360 and decreasing to 0 at \( h = 9 \) since \( 360\div40 = 9\))
Equation: \( D = 360-40h \)