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

1 answer

To find the rate of change of the number of gallons in the wading pool, you can use the formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Given the points \((1, 160)\) and \((3, 80)\), we can substitute these into the formula:

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

Substituting into the formula gives:

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

Thus, the rate of change in the number of gallons in the pool after each hour has passed is \(-40\) gallons per hour.

The correct response is: −40 gal./hr.