1. DIRECT VARIATIONS

2. What is direct variation?
When relationships of numbers are proportional, their relationships can also be called direct variation.
How do I know if data on a table is proportional? A graph?

3. How is direct variation related to constant rate of change and slope?
When two variable quantities are proportional (have a constant ratio), their relationship is called a direct variation. In a direct variation equation, the constant rate of change, or slope, is assigned a special value, k. The constant rate of change, or slope, must be simplified.
The constant ratio is called the constant of variation, or constant of proportionality.

4. Textbook p. 82
Is this line proportional? What is the slope of this line? How is it related to the direct variation?

5. Constant of Proportionality
Got it p. 82

6. Understanding the Equation
Got it p. 83

7. Determine Direct Variation
Not all situations with a constant rate of change are proportional.
Ex. Straight lines that don’t pass through the origin
Likewise, not all linear functions are direct variations.
Got it p. 83c

8. Determine Direct Variation of a Table

9. Identify the Constant of Proportionality or Constant of Variation
Write your answers as y=kx

10. Identify the Constant of Proportionality or Constant of Variation
Write your answers as y=kx

11. Identify the Constant of Proportionality or Constant of Variation
Write your answers as y=kx

12. Identify the Constant of Proportionality or Constant of Variation
Write your answers as y=kx

13. Identify the Constant of Proportionality or Constant of Variation
Write your answers as y=kx

14. Identify the Constant of Proportionality or Constant of Variation

15. Identify the Constant of Proportionality or Constant of Variation

16. Identify the Constant of Proportionality or Constant of Variation

17. Identify the Constant of Proportionality or Constant of Variation