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**Section 1 Inverse Variation**

Chapter 9 Section 1 Inverse Variation

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**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

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**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.

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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

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**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

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**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.

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**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.

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**Each ordered pair is from an inverse variation. Find the missing value.**

(2,4) and (6,y) (4,6) and (x,3)

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**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

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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

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x 0.2 0.6 1.2 y 12 4 2

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x 1 2 3 y .5

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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

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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

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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

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**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.

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**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.

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**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.

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Variation Variation describes the relationship between two or more variables. Two variables, x and y, can vary directly or inversely. Three or more variables.

Variation Variation describes the relationship between two or more variables. Two variables, x and y, can vary directly or inversely. Three or more variables.

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