1. Direct Variation
5-2

2. 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

3. 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

4. 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

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

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

7. Examples
Graph: y = -3x
Graph:

8. Writing Direct Variation Equations
Substitute variables into direct variation equation, y = kx
Solve for k
Write the direct variation equation with k

9. Examples Write a direct variation eq’n for x = 4 and y = 12.

10. Direct Variation Word Problems
Determine which value is x and which is y
Remember y varies directly with x
Substitute information into direct variation equation
Solve for k
Rewrite equation with k
If needed, substitute remaining information to solve for the required variable

11. Example
Mary’s salary varies directly with the number of hours she works. If Mary’s salary is $273 when she works 28 hours, write a direct variation equation relating these variables. How many hours would she have to work to earn $351?