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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)
and (3,80)
as (x1,y1)
and (x2,y2)
, what is the rate of change in the number of gallons in the pool after each hour has passed?

(1 point)
Responses

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

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

−40
gal./hr.
negative 40 gal./hr.

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

To determine the rate of change in the number of gallons in the pool over the time interval from \( x_1 = 1 \) to \( x_2 = 3 \) using the points \( (1, 160) \) and \( (3, 80) \), we will use the formula for the rate of change, which is given by:

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

Substituting in the values from the points:

• \( y_1 = 160 \) (gallons at \( x_1 = 1 \))
• \( y_2 = 80 \) (gallons at \( x_2 = 3 \))
• \( x_1 = 1 \)
• \( x_2 = 3 \)

Now calculate:

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

Thus, the rate of change in the number of gallons in the pool after each hour has passed is:

\(-40 \text{ gal./hr.}\)

So the correct answer is:

−40 gal./hr.