Question

sadie is participating in an open water swimming event to raise money for cancer research. she has carefully planned her pacing throughout the swim, steadily making her wa toward the finish line. there is a linear relationship between time, in minutes, since sadie started her swim, and her distance from the finish line, in meters. describe the rate of change for this relationship

Explanation:

Step1: Recall rate of change formula

The rate of change for a linear relationship (slope) is calculated as $\frac{\text{Change in } y}{\text{Change in } x}$. Here, $y$ is distance to finish line (meters) and $x$ is time (minutes).

Step2: Choose two points

Take the first two points: $(30, 4500)$ and $(60, 3000)$.

Step3: Calculate change in $y$ and $x$

Change in $y$: $3000 - 4500 = -1500$ meters.
Change in $x$: $60 - 30 = 30$ minutes.

Step4: Compute rate of change

Rate of change = $\frac{-1500}{30} = -50$ meters per minute.

Answer:

The rate of change is -50 meters per minute, meaning Sadie's distance to the finish line decreases by 50 meters every minute.