Question

for exercises 3 and 4, refer to the graphs be

1. hawk diving toward prey

a. find the constant rate of change and interpret its meaning.

b. determine whether a proportional linear relationship exists between the two quantities shown in the graph. explain your reasoning.

Explanation:

Step1: Identify two points

Choose two points on the line, say $(0,90)$ and $(10,0)$.

Step2: Calculate rate of change

The formula for the rate of change (slope) $m$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=90,x_2 = 10,y_2 = 0$. So $m=\frac{0 - 90}{10-0}=\frac{- 90}{10}=-9$. The negative sign indicates the altitude is decreasing. It means the hawk's altitude is decreasing at a rate of 9 feet per second.

Step3: Check for proportionality

A proportional linear - relationship has the form $y=kx$ and passes through the origin $(0,0)$. The graph of the hawk's dive does not pass through the origin (it starts at an altitude of 90 feet when $t = 0$). So, there is no proportional linear relationship between time and altitude.

Answer:

a. The constant rate of change is - 9 feet per second. It means the hawk's altitude is decreasing at a rate of 9 feet per second.
b. No, a proportional linear relationship does not exist. The graph does not pass through the origin $(0,0)$.