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.
40 gal./hr.
−40 gal./hr.
negative 40 gal./hr.
140 gal./hr.
Start Fraction 1 over 40 End Fraction gal./hr.
−140 gal./hr.
To find the rate of change, we need to calculate the change in the number of gallons divided by the change in time.
Let's determine the change in the number of gallons:
Change in gallons = y2 - y1 = 80 - 160 = -80 gallons
Now, let's determine the change in time:
Change in time = x2 - x1 = 3 - 1 = 2 hours
To find the rate of change, we divide the change in gallons by the change in time:
Rate of change = Change in gallons / Change in time = -80 gallons / 2 hours = -40 gallons/hour
Therefore, the rate of change in the number of gallons in the pool after each hour has passed is -40 gallons/hour.
To find the rate of change in the number of gallons in the pool after each hour has passed, we can use the formula for the slope of a line. The slope can be calculated using the following formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (1,160) and (3,80), we can plug in the values into the formula:
slope = (80 - 160) / (3 - 1)
= (-80) / 2
= -40
The slope, which represents the rate of change, is -40 gallons per hour. Therefore, the correct answer is:
The rate of change in the number of gallons in the pool after each hour has passed is -40 gal./hr.
OR
The rate of change in the number of gallons in the pool after each hour has passed is negative 40 gal./hr.
To find the rate of change, we need to calculate the difference in the number of gallons between the two points, and then divide it by the difference in time (hours) between the two points.
The initial number of gallons (y1) is 160, and after 3 hours, the number of gallons (y2) is 80.
The difference in y between the two points is 160 - 80 = 80 gallons, and the difference in x (time) is 3 - 1 = 2 hours.
Therefore, the rate of change in the number of gallons is 80 gallons / 2 hours = 40 gallons/hour.
So the correct answer is: 40 gallons/hour.