Question

car x travels 186 miles in 3 hours.
a. write the equation of the line that describes the relationship between distance and time. use x for the time in hours and y for the distance in miles.
b. what is the graph that represents the relationship between distance and time for car x? explain.
a. the equation □ describes the relationship.
(simplify your answer.)

Explanation:

Step1: Calculate speed of Car X

First, find the constant speed by dividing total distance by total time.
$\text{Speed} = \frac{186}{3} = 62$ miles per hour

Step2: Form distance-time equation

Since distance $y$ equals speed multiplied by time $x$, set up the linear equation.
$y = 62x$

Step3: Describe the graph

The equation $y=62x$ is a proportional linear relationship (passes through the origin, slope = 62).

Answer:

a. $y = 62x$
b. The graph is a straight line passing through the origin (0,0) with a slope of 62. This is because the relationship between distance and time is proportional: as time (x) increases, distance (y) increases at a constant rate of 62 miles per hour, so each unit increase in x leads to a 62-unit increase in y.