Question

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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 distance from home (mi), y 0 34 3 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

Rate of change is $\frac{\text{change in } y}{\text{change in } x}$, but we need to check the direction of change. Here, time $x$ increases from 0 to 3, and distance $y$ decreases from 34 to 10. So change in $y$ is $10 - 34 = -24$, change in $x$ is $3 - 0 = 3$.

Step2: Calculate correct rate of change

Using the formula, rate of change $= \frac{10 - 34}{3 - 0} = \frac{-24}{3} = -8$. Dylan used $34 - 10$ (positive change in $y$) instead of $10 - 34$ (negative change in $y$), so his rate of change should be negative.

Answer:

No, because the rate of change should be negative.