Question

khloe reaches the end of a hiking trail and hikes back to her car at a constant rate. after 1 hour (h), she is 8 miles (mi) from her car. after 3 h, she is 2 mi from her car. her distance from her car in miles, y, is a function of the time it takes to hike to her car in hours, x.
points on the graph: (1, 8) and (3, 2)
rate of change: -3
initial value: 11
write the equation of the function.

Explanation:

Step1: Recall linear function form

A linear function is in the form \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step2: Identify slope and intercept

We are given that the rate of change (slope \( m \)) is \(-3\) and the initial value (y - intercept \( b \)) is \( 11 \).

Step3: Substitute into linear form

Substitute \( m=-3 \) and \( b = 11 \) into the equation \( y=mx + b \). So the equation becomes \( y=-3z + 11 \) (since the independent variable is \( z \) representing time in hours and the dependent variable is \( y \) representing distance in miles).

Answer:

\( y=-3z + 11 \)