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?
40 gal./hr.
140 gal./hr.
−140 gal./hr.
−40 gal./hr.
The rate of change in the number of gallons in the pool can be determined by finding the slope of the line segment that passes through the points (1,160) and (3,80).
The formula for calculating the slope between two points is:
slope = (change in y) / (change in x)
In this case, the change in y is -80 (from 160 to 80) and the change in x is 3-1 = 2 (from 1 to 3).
So, the slope is:
slope = -80/2 = -40 gal./hr.
Therefore, the rate of change in the number of gallons in the pool after each hour has passed is -40 gal./hr. Answer: \boxed{-40 \, \text{gal./hr.}}