2.2 Direct Variation

2.2 DIRECT VARIATION

DIRECT VARIATION

Direct Variation functions have equations of the form y = kx, where k is the constant of variation and does not equal 0, x represents the input values, and y represents the output values. Many types of physical phenomena exhibit direct

variation, such as rates (miles per gallon, miles per hour, cost per pound)

DIRECT VARIATION

The graphs of direct variation functions always pass through the origin.

The formula says that the ratio of all output-input pairs equals the constant of variation, k. This is used to determine whether a function is a

direct variation function.

yk

x

IDENTIFYING DIRECT VARIATION FROM TABLES

1. Determine whether y varies directly with x, by checking the ration of all output-input pairs

2. Identify the constant of variation by simplifying

3. Plug k into

1 2

1 2

... n

n

y y y

x x x

yk

x

y kx

EXAMPLE

For each function, determine whether y varies directly with x. If so, what is the constant of variation, and the function rule?

EXAMPLE

For each function, determine whether y varies directly with x. If so, what is the constant of variation, and the function rule?

IDENTIFYING DIRECT VARIATION FROM EQUATIONS

1. Solve for y.2. If it looks like this: then it is a

direct variation y kx

EXAMPLE

For each function, determine whether y varies directly with x. If so, what is the constant of variation?

EXAMPLE

For each function, determine whether y varies directly with x. If so, what is the constant of variation?

7 14 7y x

USING A PROPORTION TO SOLVE A DIRECT VARIATION

1. Set up a proportion:

2. Fill in what you know

3. Solve for the missing piece

EXAMPLE

Suppose y varies directly with x, and y = 9 when x = -15. What is y when x = 21?

EXAMPLE

Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?

GRAPHING DIRECT VARIATION EQUATIONS The graph of a direct variation function is

always a line through the origin.

To graph a direct variation: Complete a table of values Plot the points

EXAMPLE

What is the graph of each direct variation equation?

3

4y x

EXAMPLE

What is the graph of each direct variation equation?

2y x

USING A DIRECT VARIATION TO SOLVE A PROBLEM

The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contain 200 Calories, how many Calories are in 70 grams of cheese?