Use the image to answer the question.

Question

A coordinate plane shows the x-axis, labeled as hours, ranging from 0 to 6 in increments of 1 and the y-axis, labeled as gallons, ranging from 0 to 240 in increments of 20. A line segment joins four plotted points. The coordinates of the plotted points are left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 160 right parenthesis, left parenthesis 3 comma 80 right parenthesis, and left parenthesis 5 comma 0 right parenthesis.

The graph shows the number of gallons in a wading pool that is being drained. Using the points (1,160)
(
1
,
160
)
and (3,80)
(
3
,
80
)
as (x1,y1)
(
x
1
,
y
1
)
and (x2,y2)
(
x
2
,
y
2
)
, what is the rate of change in the number of gallons in the pool after each hour has passed?

(1 point)
Responses

40 gal./hr.
40 gal./hr.

1/40
1
40
gal./hr.
Start Fraction 1 over 40 End Fraction gal./hr.

−1/40
−
1
40
gal./hr.
negative Start Fraction 1 over 40 End Fraction gal./hr.

−40
−
40

gal./hr.
negative 40 gal./hr.

Answer 1

To calculate the rate of change in the number of gallons in the pool from the points \((1, 160)\) and \((3, 80)\), we can use the formula for the slope between two points:

\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, \((x_1, y_1) = (1, 160)\) and \((x_2, y_2) = (3, 80)\).

Plugging the values into the formula gives:

\[ \text{Rate of Change} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40 \]

Thus, the rate of change in the number of gallons in the pool after each hour has passed is \(-40 \text{ gal./hr.}\)

The correct response is:

−40 gal./hr.