1. Splash Screen

2. Concept

3. Direct variation equation
If y varies directly as x and y = –15 when x = 5, find y when x = 3.
Direct variation equation
Use values that follow “if”
Solve for k
Example 1

4. Substitute the value of k back into original equation
Direct Variation
Substitute the value of k back into original equation
find y when x = 3
Answer: When x = 3, the value of y is –9.
Example 1

5. If y varies directly as x and y = 12 when x = –3, find y when x = 7.B. C. D.
Example 1

6. Concept

7. Joint variation equation
Suppose y varies jointly as x and z. Find y when x = 10 and z = 5, if y = 12 when x = 3 and z = 8.
Joint variation equation
Use values that follow “if”
Solve for k
Example 2

8. Substitute the value of k back into original equation
Joint Variation
Substitute the value of k back into original equation
Find y when x = 10 and z = 5
Answer: When x = 10 and z = 5, y = 25.
Example 2

9. Suppose y varies jointly as x and z
Suppose y varies jointly as x and z. Find y when x = 3 and z = 2, if y = 11 when x = 5 and z = 22. A. B. C. D.
Example 2

10. Concept

11. Inverse variation equation
If r varies inversely as t and r = –6 when t = 2, find r when t = –7.
Inverse variation equation
Use values that follow “if”
Solve for k
Example 3

12. Inverse Variation
Substitute the value of k back into original equation
find r when t = –7
Answer: When t = –7, r is
Example 3

13. If a varies inversely as b and a = 3 when b = 8, find a when b = 6.
C. 16
D. 144
Example 3

14. Combined variation equation
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –5, if g = 18 when h = 3 and f = 5.
Combined variation equation
Use values that follow “if”
Solve for k
Example 5

15. Substitute the value of k back into original equation
Combined Variation
Substitute the value of k back into original equation
Find g when f = 6 and h = –5
Answer: When f = 6 and h = –5, the value of g is –36.
Example 5

16. Suppose f varies directly as g, and f varies inversely as h
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –16, if g = 10 when h = 4 and f = –6.
A. –30
B. 30
C. 36
D. 40
Example 5

17. Homework p. 566 # 3 – 45 (x3)

18. End of the Lesson