Question

the table shows dylans distance from home, y, as a function of the time he rides his bicycle, x. dylan calculated the rate of change. his work is shown. is dylans work correct? yes, the rate of change is 8. no, because the rate of change should be change in x - values / change in y - values. no, because 24/3 is not 8. no, because the rate of change should be negative. time (h), x: 0, 3; distance from home (mi), y: 34, 10. dylans work: rate of change = change in y - values / change in x - values = (34 - 10)/(3 - 0) = 24/3 or 8

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) formula is $m=\frac{\text{change in }y - \text{values}}{\text{change in }x - \text{values}}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify points

Let $(x_1,y_1)=(0,34)$ and $(x_2,y_2)=(3,10)$.

Step3: Calculate rate of change

$m=\frac{10 - 34}{3-0}=\frac{- 24}{3}=-8$. Dylan's answer is positive, but the distance from home is decreasing as time increases, so the rate of change should be negative.

Answer:

No, because the rate of change should be negative.