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. what is the relationship between the change in distance and the change in time? kumikos distance from home decreases from 25 miles to 4 miles as the time increases from 0 hours to 3 hours. is the rate of change positive or negative? positive negative

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(0,25)$ and $(x_2,y_2)=(3,4)$.

Step2: Calculate the rate of change

Substitute the values into the formula: $m=\frac{4 - 25}{3-0}=\frac{- 21}{3}=-7$. Since the rate of change $m=-7<0$, the rate of change is negative.

Answer:

negative