Question

use the scenario below to answer the following multipart question
a tank full of water draining. the number of gallons in the tank is shown over time.
7 what is the rate of change?
(a) a -8
b -16
c 16
d 8
(b) what is the initial value?
a 0
b 150
c 2
d 134
(c) explain: what does the initial value mean in context of the situation?

Explanation:

Step1: Calculate rate of change

The rate of change formula for a linear relationship is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points $(x_1,y_1)=(2,134)$ and $(x_2,y_2)=(4,118)$. Then $\frac{118 - 134}{4 - 2}=\frac{- 16}{2}=-8$.

Step2: Determine initial value

The initial value is the value of $y$ when $x = 0$. Since the relationship is linear with a rate of change of - 8, if we go from $x = 2$ (where $y = 134$) to $x=0$ (decrease $x$ by 2), we increase $y$ by $2\times8 = 16$. So the initial value is $134+16 = 150$.

Step3: Explain initial value

The initial value represents the number of gallons of water in the tank at the start (time = 0) before any draining has occurred.

Answer:

(a) A. -8
(b) B. 150
(c) The initial value represents the number of gallons of water in the tank at the start (time = 0) before any draining has occurred.