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)Responses140 gal./hr.Start Fraction 1 over 40 End Fraction  gal./hr.−140 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 answer

To find the rate of change (slope) between the two points (1,160) and (3,80), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Here, we have:

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

Substituting these values into the slope 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 is \(-40 , \text{gal./hr.}\)

The correct response is therefore: −40 gal./hr.