1. Direct Variation and Proportion
Objective: Write and apply direct variation and proportion problems

3. Direct Variation
The variable y varies directly as x if there is a nonzero constant k such that y = kx. The equation y = kx is called a direct variation equation and the number k is called the constant of variation.

4. Example 1
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4.

5. Example 1
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4.
Use the direct variation equation
Substitute -24 for y and 4 for x

6. Example 1
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4.
Use the direct variation equation
Substitute -24 for y and 4 for x
Solve for k.

7. Example 1
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4.
Use the direct variation equation
Substitute -24 for y and 4 for x
Solve for k.
The direct variation equation is

8. Try This
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = 21 when x = 7.

9. Try This
Find the constant of variation, k and the direct variation equation if y varies directly as x and y = 21 when x = 7.
Use the direct variation equation
Substitute 21 for y and 7 for x
Solve for k.
The direct variation equation is

10. Example 2
Each day John rides his bike for exercise. When traveling at a constant rate, he rides 4 miles in about 20 minutes. At this rate, how long would it take John to travel 7 miles?

11. Example 2
Each day John rides his bike for exercise. When traveling at a constant rate, he rides 4 miles in about 20 minutes. At this rate, how long would it take John to travel 7 miles?

12. Example 2

13. Proportions A ratio is a comparison of two numbers by division.
A proportion is a statement that two ratios are equal.

14. Proportions A ratio is a comparison of two numbers by division.
A proportion is a statement that two ratios are equal.
A proportion of the form
can be rearranged like this:

15. Cross-Product Property
The result of what we just did is called the cross-product property of proportions. This is also called the means-extremes product property.

16. Physics Application

17. Example 3

18. Example 3

19. Example 3

20. Example 4

21. Example 4

22. Class work
In pairs/groups
Page 33
8-13

23. Homework
Pages 33-34
15-25 odd
37-51 odd