3 4 Direct Variation notes 2014.notebook
December 04, 2014
3.4 Direct Variation
Every minute that the water runs in an average shower, it
uses 6 gallons of water.
How many gallons of water do you use in the morning?
How much water would be used if you showered for:
10 minutes:
15 minutes:
20 minutes:
1
3 4 Direct Variation notes 2014.notebook
December 04, 2014
Direct Variation
2
3 4 Direct Variation notes 2014.notebook
December 04, 2014
Direct Variation
What is Direct Variation­
When one
the other
When one
the other
x
x
y
y
Examples of Direct Variation­
Formula for Direct Variation­
Examples of Direct Variation Problems­
If y = 12 when x = 15, find y when x = 20.
If y = -8 when x = -3, find x when y = 6.
3
3 4 Direct Variation notes 2014.notebook
December 04, 2014
x y
x y
2 ­6
­4 ­2
3 ­9
­2 ­1
4 ­12
2 1
5 ­15
4 2
4
3 4 Direct Variation notes 2014.notebook
December 04, 2014
if y varies directly as x
and y = 10 as x = 2.4,
find x when y =15.
5
3 4 Direct Variation notes 2014.notebook
December 04, 2014
If y varies directly as x and y = 10 find x when y =15.
6
3 4 Direct Variation notes 2014.notebook
December 04, 2014
if y varies directly as x
and y = 10 as x = 2.4, find x when y =15
7
3 4 Direct Variation notes 2014.notebook
December 04, 2014
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
8
3 4 Direct Variation notes 2014.notebook
December 04, 2014
9
3 4 Direct Variation notes 2014.notebook
December 04, 2014
Inverse Variation
10
3 4 Direct Variation notes 2014.notebook
k
y=x
December 04, 2014
or xy=k
x y
x y
x y
1 4
1 16
1 3
2 2
2 8
2 6
4 1
4 4
3 9
11
3 4 Direct Variation notes 2014.notebook
December 04, 2014
Y varies inversely as x
If y=3 when x=12, find x when y=4
12
3 4 Direct Variation notes 2014.notebook
December 04, 2014
y varies inversely as x
If y=18 when x=2, write an inverse variation equation that relates x and y.
13
3 4 Direct Variation notes 2014.notebook
December 04, 2014
y varies inversely as x
Write an inverse variation equation that realtes x and y when...
1. y= 8 when x=6
2. y=3 when x= ­10
14
3 4 Direct Variation notes 2014.notebook
December 04, 2014
y varies inversely as x
1. if y=8 when x=4, find x when y=2
2. If y=­5 when x=9, find y when x=6
15
3 4 Direct Variation notes 2014.notebook
December 04, 2014
The water level in a river varies inversely with air temperature. When the air temperature was 90 F, the water level was 11 feet. If the air temp was 110 F, what was the level of water in the river?
16
3 4 Direct Variation notes 2014.notebook
December 04, 2014
Summary:
Direct Variation
Indirect Variation 17