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Agenda Lesson 4-6 – Inverse Variation - Day 1 Standards 15.0 Use algebraic techniques Standards 16.0 Give pertinent information about given functions Warm Up Review Notes - Inverse Variation Practice Review Homework – Page 212 problems 7 to 9 and 19 to 21 all

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Warm Up Write a direct variation equation for each of the points below. Hint: y = kx 1. (4, 6) 2. (3, 9) 3. (1, 3)

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Inverse Variation Inverse Variation: A function written in the form xy = k or y = k/x where k ≠ 0 k is called the constant of variation for inverse variation The variables x and y are said to vary inversely with each other

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Writing a direct variation given a point a. Write an inverse variation equation that includes the point (5, 7). Or when x = 5 and y = 7 EXAMPLE 1 xy = k 7(5) = k Solve for k Substitute the answer for k in xy = k

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Suppose y varies inversely with x and y = 9 when x = 2. Write an inverse variation equation. You try one:

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Finding the Missing Coordinate The points (3, 8) and (2, y) are two points on the graph of an inverse variation. Find the missing value EXAMPLE 2 x 1 y 1 = x 2 y 2 3(8) = 2(y 2 ) Solve for y 2

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Class work – Please do these now Page 212 Problems 1 to 6 and 10 to 18 all Homework – Please do at home tonight Page 212 Problems 7 to 9 and 19 to 21 all

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Agenda Lesson 4-6 – Inverse Variation - Day 2 Standards 15.0 Use algebraic techniques Standards 16.0 Give pertinent information about given functions Warm Up Review Notes - Inverse Variation Practice Review Homework – Page 212 problems 30 to 35 all

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Warm Up Find the missing coordinate. Hint: x 1 y 1 = x 2 y 2 1.(5, 2) and (10, y) 2. (x, 3) and (2, 6) 3. (4, 8) and (x, 16)

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Determining Direct or Inverse Variations EXAMPLE 4 xy y/x xy 25 410 25 1230 xy y/x xy 520 10 205 254 For the table use the ratio y/x to tell whether y varies directly with x. Remember k = y/x

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For the table below, determine whether y varies directly with x. If it does, write the equation for the direct variation. You try two: xy y/x xy 49 -2-18 -6-18/3 66 Xy y/x xy 48 -9-18 214 36

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Application EXAMPLE 5 Explain whether each situation represents a direct variation or an inverse variation. a. The cost of $40.00 worth of gasoline is split among several people b. You buy several markers for 70¢ each. Cost markers Is a constant of 70¢ so this is a direct variation Total cost is a constant $40.00 so this is an inverse variation

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Class work – Please do these now Page 212 Problems 24 to 38 all Homework – Please do at home tonight Page 213 Problems 41 to 43 and 45 all

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INVERSE VARIATION Section 9.1. Solving Inverse Variation: Definition 1: A function in the form xy = k or y = k/x, where k ≠ 0, is an inverse variation.

INVERSE VARIATION Section 9.1. Solving Inverse Variation: Definition 1: A function in the form xy = k or y = k/x, where k ≠ 0, is an inverse variation.

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