Question

mel slides down waterslide a, and victor slides down waterslide b. after 2 seconds, mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. after 1 second, victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. who was descending at a faster rate?
mel: (2, 50) and (5, 35)
victor: (1, 60) and (4, 50)
mels rate of change is. that means that her height in the air decreases feet every second.
victors rate of change is. that means that his height in the air decreases feet every second.
done

Explanation:

Step1: Calculate Mel's rate of change

The formula for the rate of change (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Mel, \((x_1,y_1)=(2,50)\) and \((x_2,y_2)=(5,35)\).

$$m_{Mel}=\frac{35 - 50}{5 - 2}=\frac{- 15}{3}=-5$$

The negative sign indicates a decrease. So Mel's height in the air decreases \(5\) feet every second.

Step2: Calculate Victor's rate of change

For Victor, \((x_1,y_1)=(1,60)\) and \((x_2,y_2)=(4,50)\)

$$m_{Victor}=\frac{50 - 60}{4 - 1}=\frac{-10}{3}\approx - 3.33$$

The negative sign indicates a decrease. So Victor's height in the air decreases approximately \(3.33\) feet every second.

Answer:

Mel was descending at a faster rate. Mel's rate of change is \(-5\), meaning her height in the air decreases \(5\) feet every second. Victor's rate of change is \(-\frac{10}{3}\approx - 3.33\), meaning his height in the air decreases approximately \(3.33\) feet every second.