Unit 10: Other Non-Linear Functions
Direct Variation
Name_________________________
Date _______________ Period_____
Explore-Classwork
If you are like the average American, you have enough time to sing several songs while taking a shower.
The national average for time spent in the shower is 12.2 minutes. That means you use 73.2 gallons of
water for each shower you take. Taking one shower per day for one year would use 26,718 gallons of
water!
1.
How many gallons of water are used each minute?
2. Complete the table that shows the relationship between the time spent showering and the amount of
water used.
x (minutes)
3
6
y (gallons)
72
Shower Statistics
Write the equation that would represent the
number of gallons, y, used for a given number of
minutes, x.
4. Graph the line.
5. What does the 6 represent?
123
Amount of water used
(gallons)
3.
45
6. What is the y-intercept?
Time spent in the shower
(minutes)
The number of gallons of water used depends directly on the amount of time spent in the shower.
This means that this situation is an example of direct variation. The relationship between x and y
is constant. As one variable increases, the other variable increases proportionally.
7. What will happen to the amount of water used if you double the amount of time you spend in the
shower?
8. What will happen to the amount of water used if you spend half the amount of time in the shower?
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Unit 10: Other Non-Linear Functions
Examples of Direct Variation Graphs
Non Examples of Direct Variation Graphs
9. What do you notice about the Direct Variation graphs?
Examples of Direct Variation Equations
y = 2x
y=
1
x
2
y = 4x
Non Examples of Direct Variation Equations
y=x
y = 2x + 1
y=
1
x+4
2
y = 4x - 2
y=x+3
10. What do you notice about the proportional equations?
Examples of Direct Variation Tables
x
0
2
3
6
10
n
y
0
6
9
18
30
x
5
10
15
30
50
n
y
10
20
30
60
100
x
-2
-1
0
1
2
n
Non Examples of Direct Variation Tables
y
-8
-4
0
4
8
x
0
1
2
3
4
y
3
6
9
12
15
x
5
10
15
20
25
y
30
40
50
60
70
x
-2
-1
0
1
2
y
0
-1
-2
-3
-4
11. Choose one of the direct variation tables. Divide each y value by the x value. What do you notice?
12. Write the equation for each direct variation table.
In each of the following problems, the value of y varies directly with x. Write the direct variation
equation.
1. y = 15, x = 3
6. y = -8, x -1
7. y = 6, x = 12
8. y = 9, x = 12
9. y = 14, x = 9
10. y =
18
5
,
x = 20
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