4 of 54 of 5 Items
Question
Use the image to answer the 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
−40
gal./hr.
negative 40 gal./hr.
140
gal./hr.
Start Fraction 1 over 40 End Fraction gal./hr.
40 gal./hr.
40 gal./hr.
−140
gal./hr.
1 answer
To find the rate of change between the two points \((1, 160)\) and \((3, 80)\), we can use the formula for the slope (rate of change):
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (1, 160)\) and \((x_2, y_2) = (3, 80)\).
Now, plug in the values:
\[ \text{slope} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40 \]
So the rate of change in the number of gallons in the pool after each hour has passed is:
\(-40 , \text{gal./hr.}\)
The correct response is:
−40 gal./hr.
