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? no, because the rate of change should be negative. what is the correct rate of change? rate of change: dylans work rate of change = \frac{change in y - values}{change in x - values}=\frac{34 - 10}{3 - 0}=\frac{24}{3} or 8

Explanation:

Step1: Identify the formula for rate of change

The rate of change formula is $\text{rate of change}=\frac{\text{change in }y - \text{values}}{\text{change in }x - \text{values}}$.

Step2: Determine the correct change in values

As time ($x$) increases from $0$ to $3$ hours, the distance from home ($y$) decreases from $34$ miles to $10$ miles. So the change in $y$ - values is $10 - 34=- 24$ and the change in $x$ - values is $3 - 0 = 3$.

Step3: Calculate the rate of change

$\text{rate of change}=\frac{10 - 34}{3 - 0}=\frac{-24}{3}=-8$.

Answer:

-8