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
−1/40 gal./hr.
negative Start Fraction 1 over 40 End Fraction gal./hr.
1/40 gal./hr.
Start Fraction 1 over 40 End Fraction gal./hr.
−40 gal./hr.
negative 40 gal./hr.
40 gal./hr.
40 gal./hr.
To find the rate of change, we need to calculate the slope of the line segment between the points (1,160) and (3,80). The slope is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the given coordinates into the formula, we get:
slope = (80 - 160) / (3 - 1)
slope = (-80) / 2
slope = -40
So, the rate of change in the number of gallons in the pool after each hour has passed is -40 gal/hr.
Therefore, the correct answer is: -40 gal/hr.
is this correct?
Apologies for the miscalculation. Let's recalculate the slope correctly:
slope = (y2 - y1) / (x2 - x1)
= (80 - 160) / (3 - 1)
= (-80) / 2
= -40
So, the rate of change in the number of gallons in the pool after each hour has passed is indeed -40 gal/hr.
Therefore, the correct answer is: -40 gal/hr.