5 – 4 A: Direct Variation

Homework Review

A line has a slope of 5 and passes through the points (4,3) and (2,y). What is the value of y?

y = -7

Homework Review

A line passes through the origin and has a slope of .

Through which quadrants does the line pass?

II and IV

Definitions

Direct variation – linear relationship between two variables that can be written in the form y = kx

Constant of variation – the fixed number (k) in a direct variation (the coefficient)

**This is another expression that means slope or rate of change.***

Direct Variation

• Will be a straight line when graphed

• ALWAYS passes through the origin (0,0)

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y = 2x

Yes

k = 2

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y = 1/3 x

Yes

k = 1/3

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y = - ½x

Yes

k = -½

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y = 2x + 3

No

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y = ½x - 6

No

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

2y = x

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

2y = x

2 2

y = ½ x

Yes, this is a direct variation.

½ is the constant of variation.

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y + 1 = 2x .

Identifying a Direct Variation from an Equation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

y + 1 = 2x Solve for y.

- 1 - 1 .

y = 2x – 1 .

This is not in the form y = kx, so this is not a direct variation.

Work with your partner.

Page 214 (1-4)

Notes:

The graph of a direct variation is a line that passes through the origin (0 0).

The constant of variation (k) is the slope of the line.

Does this graph represent a direct variation?

• Yes, the line passes through the origin, so this is a direct variation.

• What is the slope of the line (constant of variation)?

k = 1

Does this graph represent a direct variation?

• Yes, the line passes through the origin, so this is a direct variation.

• What is the constant of variation?

k = -½

Does this graph represent a direct variation?

• No, the line does not pass through the origin, so this is NOT a direct variation.

Does this graph represent a direct variation?

• No, the line does not pass through the origin, so this is NOT a direct variation.

Does this graph represent a direct variation?

• Yes, the line passes through the origin, so this is a direct variation.

• What is the constant of variation?

k = 2

y = 2x0 1 2 3 4 5 6 7 8 9 10

22

20

18

16

14

12

10

8

6

4

2

0

Does this graph represent a direct variation?

• No, this is not a straight line, so this is NOT a direct variation.

Let’ look at:

Page 214 (7-8)

Partner Talk

Page 215 (19-24)

Homework:

Page 214 (10-13, 16-17)