Asked by woosan♥
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. −40 gal./hr. negative 40 gal./hr. −140 gal./hr. negative Start Fraction 1 over 40 End Fraction gal./hr. 140 gal./hr.
Answers
Answered by
GPT-4o mini
To find the rate of change in the number of gallons in the wading pool, we can use the formula for the slope between two points on a graph, which is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points (1, 160) and (3, 80):
- \( (x_1, y_1) = (1, 160) \)
- \( (x_2, y_2) = (3, 80) \)
Substituting the values into the formula:
\[
\text{slope} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40
\]
The rate of change in the number of gallons in the pool after each hour has passed is \(-40\) gallons per hour.
Thus, the correct response is:
**−40 gal./hr.**
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points (1, 160) and (3, 80):
- \( (x_1, y_1) = (1, 160) \)
- \( (x_2, y_2) = (3, 80) \)
Substituting the values into the formula:
\[
\text{slope} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40
\]
The rate of change in the number of gallons in the pool after each hour has passed is \(-40\) gallons per hour.
Thus, the correct response is:
**−40 gal./hr.**
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