1. Direct Variation
Lesson 34

2. Objectives
HSA-CED.2(2): Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scale.

3. Example; find direct variation
Suppose y varies directly as x and y = 32 when x = -4.
a) Write an equation relating x and y.
b) Find x when y = -64.
a) Relate x and y
y = kx
y = kx
(32) = k(-4)
y = -8x
-8 = k
b) Find x when y= -64
-64 = -8x
x = 8

4. Example; find direct variation
If y varies directly as x and y = 3 when x = -9,
a) Write an equation relating x and y.
b) Find x when y = 5.
a) Relate x and y
y = kx
y = kx
(3) = k(-9)
y = -(1/3)x
-(1/3) = k
b) Find x when y= 5
5 = -(1/3)x
x = -15

5. Example; find direct variation
A soap manufacturing company packs 52 soaps per carton. The amount of soap varies directly as the number of cartons packed. Find the number of soaps that can be packed in 10 cartons.
s varies directly as c
s = kc
s = 52c
Find s when c = 10
s = 52(10)
s = 520 soaps

6. Example; find direct variation
The number of gallons of gas varies directly with the number of miles the jeep runs. A jeep runs 18 mi. on 2 gallons of gas. How many miles will the car run on 4.4 gallons of gas?
g varies directly as m
Graph the situation.
g = km 18 36 54 4 2 6 8
Miles
Gas
(2) = k(18)
k = 1/9
g = (1/9)m
Find m when g = 4.4
4.4 = (1/9)(m)
m = 39.6 miles

7. #34: Direct Variation Questions? Summarize Notes Homework
Google Classroom
Quiz