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Agenda Lesson 4-6 – Inverse Variation - Day 1PowerPoint Presentation

Agenda Lesson 4-6 – Inverse Variation - Day 1

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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

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: 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

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

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

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

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

Find the missing coordinate. Hint: x1y1 = x2y2

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

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

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

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