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Agenda Lesson 4-6 – Inverse Variation - Day 1

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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

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)

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

1

EXAMPLE

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

xy = k

7(5) = k

Solve for k

Substitute the answer for k in xy = k

You try one:

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

2

EXAMPLE

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

x1y1 = x2y2

3(8) = 2(y2)

Solve for y2

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

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

Warm Up

Find the missing coordinate. Hint: x1y1 = x2y2

- (5, 2) and (10, y)
- (x, 3) and (2, 6)
- 3. (4, 8) and (x, 16)

4

EXAMPLE

Determining Direct or Inverse Variations

For the table use the ratio y/x to tell whether y varies directly with x. Remember k = y/x

You try two:

For the table below, determine whether y varies directly with x. If it does, write the equation for the direct variation.

5

EXAMPLE

Cost

markers

Is a constant of 70¢ so this is a direct variation

Application

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

Total cost is a constant $40.00 so this is an inverse variation

b. You buy several markers for 70¢ each.

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