Question

use the scenario below to answer the following multipart question
time water
2 134
4 118
6 102
8 86
a tank full of water draining. the number of gallons in the tank is shown over time.
(a) what is the rate of change?
(a) -16
(b) 16
(c) 8
(d) -8
(b) what is the initial value?
(a) 134
(b) 2
(c) 0
(d) 150
(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 $x$ be time and $y$ be the amount of water. Using the points $(2,134)$ and $(4,118)$: $\frac{118 - 134}{4 - 2}=\frac{-16}{2}=-8$.

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 $-8$, going from $x = 2$ where $y = 134$ to $x = 0$, we add $2\times8$ to 134. So the initial value is $134+16 = 150$.

Step3: Explain initial value

The initial value represents the amount of water in the tank at the start (time $t = 0$) before any water has drained.

Answer:

(a) D. -8
(b) D. 150
(c) The initial value represents the number of gallons of water in the tank at the start (time $t = 0$) before any water has drained.