To find an equation that represents Khloe's distance from her car as a function of time, we can use the given information to determine the relationship.
We have two points based on the information provided:
- After 1 hour (x = 1), Khloe is 8 miles from her car (y = 8).
- After 3 hours (x = 3), Khloe is 2 miles from her car (y = 2).
We can form the linear equation \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
First, we will calculate the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 8}{3 - 1} = \frac{-6}{2} = -3 \]
Now we know the slope is -3. We can use one of the points to find the y-intercept \(b\). We'll use the point (1, 8):
\[ y = mx + b \implies 8 = -3(1) + b \implies 8 = -3 + b \implies b = 8 + 3 = 11 \]
Now we have both \(m\) and \(b\). The equation for Khloe's distance from her car as a function of time is:
\[ y = -3x + 11 \]
This equation means that for every hour \(x\) that passes, Kim's distance \(y\) from her car decreases by 3 miles, starting from 11 miles when she first began her hike.