Question

Jordan will hike the trail shown at a rate of 3 mi/h. Write a linear equation to represent the distance Jordan still has to walk after x hours. What does the y-intercept of the equation represent?

A. The y-intercept represents the initial distance Jordan has already hiked.
B. The y-intercept represents the rate at which Jordan is hiking.
C. The y-intercept represents the total distance of the trail.
D. The y-intercept represents the remaining distance Jordan has to walk after starting.

Answer 1

Jordan's remaining distance to walk after x hours can be represented by the linear equation y = D - 3x. The y-intercept represents the total distance of the trail, which is the starting distance Jordan has yet to hike (option C).

Step-by-step explanation:

To represent Jordan's remaining distance to walk after x hours at a rate of 3 miles per hour (mi/h), we can use a linear equation. Let's denote the total distance of the trail as D. After x hours, Jordan would have walked 3x miles. Therefore, the remaining distance is D - 3x. The linear equation that represents this is y = D - 3x, where y is the remaining distance and x is the number of hours hiked.

The y-intercept of this equation would be the value of y when x equals 0. Since x represents the hours hiked, at x=0, Jordan has just started and the full distance of the trail is ahead. Thus, the y-intercept represents the total distance of the trail, which corresponds to option C: The y-intercept represents the total distance of the trail.

As an additional example, consider the equation y = 55x + 75 provided earlier, where the slope is 55, representing the rate, and the y-intercept is 75, most likely representing some fixed starting fee. In this context, the slope indicates an increase of $55 to the total charge for every additional hour worked, and the intercept is the initial fee before any hours are worked.