Holt Algebra 1

5-5 Direct Variation

Use a graph of the function

to find the value of f(x) when x = –4. Check

your answer. y

x

4,6

14 4 4 6

2f

Holt Algebra 1

5-5 Direct Variation

Identify, write, and graph direct variation.

Objective

Holt Algebra 1

5-5 Direct Variation

A recipe for paella calls for 1 cup of rice to make 5 servings.

5y x " varies directly with "y x

Holt Algebra 1

5-5 Direct Variation

A direct variation is a special type of linear relationship that can be written in the form y = kx, where k is a nonzero constant called the constant of variation.

Holt Algebra 1

5-5 Direct Variation

Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 3x

3x + y = 8

3k

3x 3x3 8y x

–4x + 3y = 0

3 8 does not

represent direct variation.

x y

4x 4x3 4y x

4

3y x

4

3k

Holt Algebra 1

5-5 Direct Variation

Tell whether each equation represents a direct variation. If so, identify the constant of variation.3y = 4x + 1

3x = –4y

3 3 3

4 1

3 3y x

3 4 1 does not

represent direct variation.

y x

4 4

3

4y x

3

4k

Holt Algebra 1

5-5 Direct Variation

So, in a direct variation, the ratio is equal to the constant of variation.

What happens if you solve y = kx for k?

x x

yk

x

Holt Algebra 1

5-5 Direct Variation

Tell whether the relationship is a direct variation. Explain.

The relationship represents

direct variation. 3.y

kx

Holt Algebra 1

5-5 Direct Variation

Tell whether each relationship is a direct variation. If it is, explain.

The relationship represents

direct variation. 4.y

kx

Holt Algebra 1

5-5 Direct Variation

The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21.

3

9

y

x

3

21 9

y

9 63y 7y

Holt Algebra 1

5-5 Direct Variation

2y x

A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph.

1 2 3 4 5 x(h) time

dist

ance

(m

i)

y

369

12# of hoursx

Holt Algebra 1

5-5 Direct Variation

The perimeter y of a square varies directly with its side length x. Write a direct variation equation for this relationship. Then graph.

HW pp. 329-331/11-43 Odd,46-55 

x

x

x

x

4P x x

1 2 3 4 5 xside length

Per

imet

er

P x

5101520