Question

car x travels 174 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 58x describes the relationship.
(simplify your answer.)

Explanation:

Part a

Step 1: Find the speed (slope)

The speed of the car is the distance traveled divided by time. So, speed $v = \frac{174}{3} = 58$ miles per hour.

Step 2: Write the linear equation

The relationship between distance $y$ and time $x$ is linear, and the equation of a line is $y = mx + b$. Since the car starts at distance 0 (when time $x = 0$), $b = 0$. The slope $m$ is the speed, so $y = 58x$.

The relationship between distance and time for Car X is linear (since distance = speed×time, and speed is constant here). A linear relationship with a positive slope (as speed is positive, meaning distance increases with time) and passing through the origin (when time is 0, distance is 0) is represented by a straight line passing through the origin with a slope of 58. So the graph is a straight line starting at the origin (0,0) and having a slope of 58, showing a proportional relationship between distance and time (direct variation).

Answer:

$y = 58x$

Part b