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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?

User Stylesuxx
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Final answer:

A linear equation to represent the distance Jordan still has to walk after x hours at a rate of 3 mi/h is y = total initial distance - 3x. The y-intercept is the total initial distance, and the slope of the equation is 3, representing the hiking rate per hour.

Step-by-step explanation:

The student is asking for a linear equation to represent the distance Jordan has still to walk after x hours of hiking at a rate of 3 mi/h.

To construct this equation, let's assume that y represents the distance remaining. If the initial distance to be hiked is not given, we can't know the actual distance left without that value.

But we can create a general equation: y = total initial distance - 3x, where total initial distance is the y-intercept and represents the total distance Jordan has to hike when x equals 0, and 3 is the slope of the line, representing the rate at which Jordan is hiking (3 mi/h).

For example, if the total distance to be hiked was 9 miles, the equation would be y = 9 - 3x. Here, the y-intercept is 9, which represents the total distance Jordan has to hike before he starts.

As Jordan hikes, the value of x (the number of hours hiked) increases, and the value of y (the distance remaining) decreases linearly.

User Dan Hlavenka
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