Question

kumiko rides home on her bike. her distance from home in miles, y, is a function of the time she rides her bike in hours, x. the graph of the function passes through the points (0,25) and (3,4). the initial value is 25. it represents the distance kumiko is from home when she starts biking. the rate of change is -7. kumiko bikes toward home at a rate of 7 miles per hour. write an equation to represent kumikos distance from home, y. y = x + ?

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Identify values

We know the rate of change $m=-7$ (from the previous calculation in the problem) and the initial value $b = 25$ (the distance from home when she starts biking).

Answer:

$y=-7x + 25$