4.6
Direct Variation
How much do 36 gold bars weigh?
Goal
Write and graph
equations that represent
direct variation.
If you know the weight of one standard mint
gold bar, then you can determine the weight
of 2, 3, or more gold bars. In Example 3 you
will see that total weight is directly
proportional to the number of bars.
Key Words
• direct variation
• constant of variation
• origin
When two quantities y and x have a constant ratio k, they are said to have
direct variation. The constant k is called the constant of variation.
y
x
If k, then y kx.
Model for Direct Variation:
EXAMPLE
Student Help
READING ALGEBRA
The model for direct
variation y kx is
read as “y varies
directly with x.”
1
y
x
y kx or k, where k 0.
Write a Direct Variation Model
The variables x and y vary directly. One pair of values is x 5 and y 20.
a. Write an equation that relates x and y.
b. Find the value of y when x 12.
Solution
a. Because x and y vary directly, the equation is in the form of y kx.
y kx
20 k(5)
4k
ANSWER 䊳
b. y 4(12)
y 48
ANSWER 䊳
Write model for direct variation.
Substitute 5 for x and 20 for y.
Divide each side by 5.
An equation that relates x and y is y 4x.
Substitute 12 for x.
Simplify.
When x 12, y 48.
Write a Direct Variation Model
The variables x and y vary directly. Use the given values to write a direct
variation model that relates x and y.
1. x 2, y 6
236
Chapter 4
Graphing Linear Equations and Functions
2. x 3, y 21
3. x 8, y 96