2.2 Direct Variation
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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?