Holt Algebra 1

5-5 Direct Variation

Students will be able to: Identify, write, and graph direct variation.

Learning Target

Holt Algebra 1

5-5 Direct VariationA recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings.

5y x or " 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 VariationTell 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 notrepresent direct variation.x y

4x 4x3 4y x

43

y x43

k

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

ykx

Holt Algebra 1

5-5 Direct VariationTell whether the relationship is a direct variation. Explain.

The relationship represents

direct variation. 3.ykx

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.ykx

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.

39

yx

3

21 9y

9 63y 7y

Holt Algebra 1

5-5 Direct VariationA 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.

2y x1 2 3 4 5 x

(h) time

dist

ance

(mi)

y

369

12

Holt Algebra 1

5-5 Direct VariationThe perimeter y of a square varies directly with its side length x. Write a direct variation equation for this relationship. Then graph.

HW pp. TBD 

x

x

x

x

4P x x

1 2 3 4 5 xside length

Per

imet

er

P x

5101520

Holt Algebra 1

5-5 Direct Variation

Write a linear equation in slope-intercept form.Graph a line using slope-intercept form.

Learning Targets

Holt Algebra 1

5-5 Direct VariationGraph the line given the slope and y-intercept.

y intercept = 4

x

y25

RISERUN

25

Holt Algebra 1

5-5 Direct VariationGraph the line given the slope and y-intercept.

x

yslope = 4; y-intercept =

41

RISERUN

4

1

Holt Algebra 1

5-5 Direct VariationGraph the line given the slope and y-intercept.

slope = 2, y-intercept = –3

x

y

21

RISERUN

21

Holt Algebra 1

5-5 Direct VariationGraph the line given the slope and y-intercept.

slope = , y-intercept = 1

x

y

23

RISERUN

23

Holt Algebra 1

5-5 Direct Variation

Write the equation that describes the line in slope-intercept form. slope = ; y-intercept = 4

1 44

y

y mx b

x

Holt Algebra 1

5-5 Direct VariationWrite the equation that describes the line in slope-intercept form.

slope = –9; y-intercept =

594

mx b

y

y

x

Holt Algebra 1

5-5 Direct Variation

slope = 2; (3, 4) is on the line

Write the equation that describes the line in slope-intercept form.

4 2 3y mx b

b

4 6 b

662 b

2 2y x

Holt Algebra 1

5-5 Direct Variation

Graph the line described by the equation. y = 3x – 1

x

y

31

RISERUN

31

Holt Algebra 1

5-5 Direct Variation

3 32

y x

Graph the line described by the equation.

x

y2y + 3x = 63x 3x

2 3 6y x 2 2 2

32

RISERUN

3

2

Holt Algebra 1

5-5 Direct Variation

0 4ymx

y x b

Graph the line described by the equation.

y = –4

x

y

HW pp. 329/10-34 even & pp. 338-340/13-29,31