ARate: 10 gallons per minute Is the Ratio Constant? Yes
B
Cy=10x
Practice makes perfect
We are told that the rate at which Robert fills the pool is 10 gallons per minute. Since he fills the pool with the same amount of water each minute, the rate is constant.
Rate=10gal/1min
We are asked to graph the given relationship on the coordinate plane. Let's start by making a table to find the amount of water in the pool after 0, 1, 2, 3, and 4 minutes.
Time (h)
0
1
2
3
4
Water Amount (gal)
We know that Robert fills the pool at a rate of 10 gallons each minute. Let's use this information to complete the table.
Time (h)
0
1
2
3
4
Water Amount (gal)
10(0)=0
10(1)=10
10(2)=20
10(3)=30
10(4)=40
Let's write the two quantities as ordered pairs where the x-coordinate is the time and the y-coordinate is the amount of water in the pool.
Time (h)
0
1
2
3
4
Water Amounts (gal)
0
10
20
30
40
(time, water amounts)
(0,0)
(1,10)
(2,20)
(3,30)
(4,40)
Now we can graph the ordered pairs on the coordinate plane.
Finally, let's connect the ordered pairs and extend the line to the y-axis.
We are asked to write an equation for the direct variation. Recall that a direct variation is a relationship in which the ratio of y to x is constant, k. An equation for a direct variation follows a specific format.
y = kx, k≠0
In this case, x is the time in minutes and y is the amount of water in gallons that is in the pool after x minutes. Since Robert fills the pool at the constant rate of 10 gallons per minute, k is equal to 10. Let's use this information to write the equation for the direct variation.
y = 10x
