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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 Variation
A 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 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
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
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.
2y x1 2 3 4 5 x
(h) time
dist
ance
(m
i)
y
369
12
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. 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 Variation
Graph the line given the slope and y-intercept.
y intercept = 4
x
y2
5
RISE
RUN
25
Holt Algebra 1
5-5 Direct Variation
Graph the line given the slope and y-intercept.
x
yslope = 4; y-intercept =
4
1
RISE
RUN
4
1
Holt Algebra 1
5-5 Direct Variation
Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3
x
y
2
1
RISE
RUN
2
1
Holt Algebra 1
5-5 Direct Variation
Graph the line given the slope and y-intercept.
slope = , y-intercept = 1
x
y
2
3
RISE
RUN
23
Holt Algebra 1
5-5 Direct Variation
Write the equation that describes the line in slope-intercept form.
slope = ; y-intercept = 4
14
4y
y mx b
x
Holt Algebra 1
5-5 Direct Variation
Write the equation that describes the line in slope-intercept form.
slope = –9; y-intercept =
59
4
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 3
y 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
3
1
RISE
RUN
3
1
Holt Algebra 1
5-5 Direct Variation
33
2y x
Graph the line described by the equation.
x
y2y + 3x = 6
3x 3x2 3 6y x 2 2 2
3
2
RISE
RUN
3
2
Holt Algebra 1
5-5 Direct Variation
0 4y
m
x
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
