1. Direct Variation
Section 1.9

2. Notes: Direct Variation
When two variable quantities have a constant ratio, their relationship is called a ________________.
The constant ratio is called the _____________________.
The constant of variation is also known as the _____________________.

3. What is a Direct Variation?
A special equation in the form: y = kx
k is called the “constant of variation”; it is also the slope of the equation
The variables have a direct relationship; as one increases/decreases, so does the other
The graph of a direct variation always passes through the origin
Example: y = 3x

4. Determining a Direct Variation
FROM EQUATIONS:
Put equation into form (y = ) and determine if it fits the pattern y = kx
Are these direct variations?
y = x y = 2x – x = 5y

5. Notes: Determine a Direct Variation
Not all situations with a constant rate of change are proportional relationships.
Likewise, not all linear functions are direct variations.

6. Determining a Direct Variation
FROM TABLES:
Solve each ordered pair for k (k = y/x)
If k is constant for each ordered pair, you have a direct variation

7. Examples X Y -6 9 1
-1.5 8
-12 X Y -2 1 3 6 8 -4

8. Graphing Direct Variations
Always know 1 point on the line: (0,0)
Use k (the slope) to get additional points

9. Examples: Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality 1.
Pictures, x 3 4 5
Profit, y 24 32 40

10. Year, x 5 10 15
Height, y
12.5 25
37.5

11. Essential Question
How can you determine if a linear relationship is a direct variation from an equation? A table? A graph?
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _________