Use the image to answer the question.

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

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

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

−40 gal./hr.
negative 40 gal./hr.

−140 gal./hr.

1 answer

To find the rate of change in the number of gallons in the wading pool after each hour, we can use the formula for the slope between two points:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((x_1, y_1) = (1, 160)\) and \((x_2, y_2) = (3, 80)\):

\[ y_1 = 160, \quad y_2 = 80, \quad x_1 = 1, \quad x_2 = 3 \]

Plugging in the values:

\[ \text{slope} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40 \]

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

\[ \text{-40 gal./hr.} \]

So the correct response is:

−40 gal./hr.