Question

1. use the graph to answer the questions below. a. the rate of change between 0 and 2 hours is _ b. the rate of change between 2 and 5 hours is _ c. the rate of change between 5 and 9 hours is _ d. the heaviest rain fell during which time - period? _

Explanation:

Step1: Recall rate - of - change formula

The rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$ on a graph is given by $\frac{y_2 - y_1}{x_2 - x_1}$, where $x$ represents time and $y$ represents the amount of rain.

Step2: Calculate rate of change for 0 - 2 hours

Let $(x_1,y_1)=(0,12)$ and $(x_2,y_2)=(2,10)$. Rate of change $=\frac{10 - 12}{2-0}=\frac{- 2}{2}=-1$.

Step3: Calculate rate of change for 2 - 5 hours

Let $(x_1,y_1)=(2,10)$ and $(x_2,y_2)=(5,7)$. Rate of change $=\frac{7 - 10}{5 - 2}=\frac{-3}{3}=-1$.

Step4: Calculate rate of change for 5 - 9 hours

Let $(x_1,y_1)=(5,7)$ and $(x_2,y_2)=(9,3)$. Rate of change $=\frac{3 - 7}{9 - 5}=\frac{-4}{4}=-1$.

Step5: Determine heaviest rain

The steepest part of the graph represents the heaviest rain. The slope is constant in this case, but we can also note that the amount of rain changes most in the last interval in terms of the overall decrease. Looking at the graph, we can see that the line is steeper towards the end. The time - interval with the heaviest rain is 5 - 9 hours as the amount of rain decreases by 4 inches in 4 hours compared to 2 inches in 2 hours or 3 inches in 3 hours in other intervals.

Answer:

a. - 1
b. - 1
c. - 1
d. 5 - 9 hours