1. Section 1 Inverse Variation
Chapter 9
Section 1
Inverse Variation

2. Direct Variation (from Ch. 2)
Direct Variation – a linear function defined by an equation of the form y = kx, where k ≠ 0
Constant of Variation is represented by k
How would you solve for k?
Notice that as x increases so does y

3. Identifying a Direct Variation from a Table
Remember
For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. b) a) x y 1 4 2 7 5 16 x y 2 8 3 12 5 20
Since the ratios are not equal this is not a direct variation.
y does not vary directly with x.
Since the fractions are equal, the constant of variation (k) is 4. The equation is y = 4x.

4. Inverse Variation
An inverse Variation is a function of the form where k ≠ 0
How would you solve for k?
k = yx
Notice that if x increases, y decreases

5. Suppose that x and y vary inversely, and x = 3 when y = -5
Suppose that x and y vary inversely, and x = 3 when y = -5. Write the function that models this situation.
Write the general form
Substitute the values of x and y
Solve for k
Put it in the general form

6. Suppose that x and y vary inversely, and x = 0. 3 when y = 1. 4
Suppose that x and y vary inversely, and x = 0.3 when y = 1.4. Write the function that models the variation.

7. Suppose that x and y vary inversely, and x = 7 when y = 4
Suppose that x and y vary inversely, and x = 7 when y = 4. Write the function that models the variation.

8. Each ordered pair is from an inverse variation. Find the missing value.
(2,4) and (6,y)
(4,6) and (x,3)

9. Identifying Direct and Inverse Variations from x-y charts
Divide each pair to see if the relation is Direct
Multiply each pair to see if the relation is Inverse
If Neither work answer neither

10. Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write the function to model the direct and inverse variations. A) x
0.5 2 6 y
1.5 18

11. x
0.2
0.6
1.2 y 12 4 2

12. x 1 2 3 y .5

13. Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write the function to model the direct and inverse variations. A) x
0.8
0.6
0.4 y
0.9
1.2
1.8 x 2 4 6 y
3.2
1.6
1.1 B) C) x
1.2
1.4
1.6 y 18 21 24

14. Combined Variations
Combined Variations include direct and inverse variations in more complicated relationships
Notice that all the general forms have a k, but it is not mentioned in the words
DO NOT WRITE THE BULLETS BELOW
Copy the chart on the next slide on a notecard – you will be able to use this on the test
Note that the variables and constants used are examples –these are guidelines for the questions you will need to answer, not an all inclusive list

15. Combined Variation
Equation Form
y varies directly with the square of x
y varies inversely with the cube of x
z varies jointly with x and y
z varies jointly with x and y and inversely with w
z varies directly with x and inversely with the product of w and y

16. Write the function that models each relationship
Write the function that models each relationship. Find z when x = 4 and y = 9
z varies directly with the square of x and inversely with y. When x = 2, and y = 4, z = 3.
Write a variation, using the chart if necessary. Don’t forget the k.
Substitute known values
Solve for k
Rewrite general variation substituting in the number for k.

17. Write the function that models each relationship
Write the function that models each relationship. Find z when x = 4 and y = 9
z varies directly with x and inversely with y. When x = 6 and y = 2, z = 15.
z varies jointly with x and y. when x =2 and y = 3, z = 60.

18. Homework Workbook Show all work, don’t take the shortcut
Practice # 1-32 all
Show all work, don’t take the shortcut
Remember that sometimes x and y are presented in (x, y) format. Use your head and think of the information given.