A water tank is being drained at a constant rate. After 2 hours of draining, the tank cont… — ACT

A water tank is being drained at a constant rate. After $2$ hours of draining, the tank contains $140$ gallons of water, and after $5$ hours, it contains $80$ gallons. When the relationship between the time spent draining, $t$ , and the volume of water, $v$ , is plotted on a standard coordinate plane with $t$ on the horizontal axis, what is the slope of the resulting line?

A
$-60$
$-20$ Answer
C
$-\frac{1}{20}$
D
$20$
E
$60$

Answer

The slope of the line is

-20

The correct answer is

-20

. The slope represents the rate of change of the volume of water with respect to time. Using the points

(2, 140)

and

(5, 80)

, the slope is calculated as the change in volume divided by the change in time:

\frac{80 - 140}{5 - 2} = \frac{-60}{3} = -20

Step-by-Step Solution

Identify the coordinates of the two data points from the problem context.

The two points are

(2, 140)

and

(5, 80)

, where time

t

represents the horizontal coordinate and volume

v

represents the vertical coordinate.

The problem defines the horizontal axis as representing time

t

and the vertical axis as representing volume

v

Apply the slope formula

m = \frac{v_2 - v_1}{t_2 - t_1}

using the coordinates from Step 1.

m = \frac{80 - 140}{5 - 2} = \frac{-60}{3} = -20

Calculating the ratio of change in the vertical axis to the change in the horizontal axis gives the slope of the line.

Key Concept

Slope as a constant rate of change in a linear relationship

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