1. 2.2 DIRECT VARIATION

2. DIRECT VARIATION

3. DIRECT VARIATION
 The graphs of direct variation functions always
pass through the origin.
y
 The formula = k says that the ratio of all
x
output-input pairs equals the constant of
variation, k.
 This is used to determine whether a function is a
direct variation function.

4. IDENTIFYING DIRECT
VARIATION FROM TABLES
1. Determine whether y varies directly with x, by
checking the ratio of all output-input pairs
y1 y2 yn
= = ... =
x1 x2 xn
2. Identify the constant of variation by
simplifying y
=k
x
3. Plug k into y = kx

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

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

7. IDENTIFYING DIRECT
VARIATION FROM
EQUATIONS
y = kx

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

9. EXAMPLE
 For each function, determine whether y varies
directly with x. If so, what is the constant of
variation?
7 y = 14 x + 7

10. 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

11. EXAMPLE

12. EXAMPLE

13. 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
OR
 Use the origin and the slope

14. EXAMPLE
 What is the graph of each direct variation
equation?
3
y= x
4

15. EXAMPLE
 What is the graph of each direct variation
equation?
y = −2 x

16. 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?

17. HOMEWORK
 Page 71
 #2,3
 #7 – 45 odd