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 \\(\square\\) describes the relationship.
(simplify your answer)

Explanation:

Part (a)

Step1: Find the speed (slope)

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

Step2: Write the linear equation

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

The relationship between distance and time for Car X is linear (as speed is constant, $y = 58x$). A linear relationship with a positive slope (since speed is positive) and passing through the origin (when $x = 0$, $y = 0$) is represented by a straight line passing through the origin with a slope of 58. This is because for every hour (increase in $x$), the distance ($y$) increases by 58 miles, so the graph is a straight line with a constant rate of change (slope) and starts at (0,0).

Answer:

$y = 58x$

Part (b)