5-5
Direct Variation
Learning Target
Students will be able to: Identify, write, and
graph direct variation.
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.
 y  5x
or " y varies directly w ith 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
k 3
3x + y = 8
3 x  y  8 does not
3x
3x
y  3x  8
represent direct variation.
–4x + 3y = 0
4 x
4 x
3y  4x
Holt Algebra 1
y
4
3
x
k 
4
3
5-5
Direct Variation
What happens if you solve y = kx for k?
x
k 
x
y
x
So, in a direct variation, the ratio
the constant of variation.
Holt Algebra 1
is equal to
5-5
Direct Variation
Tell whether the relationship
is a direct variation. Explain.
T h e relatio n sh ip rep resen ts
d irect variatio n . k 
y
x
Holt Algebra 1
 3.
5-5
Direct Variation
Tell whether each relationship is a
direct variation. If it is, explain.
T h e relatio n sh ip rep resen ts
d irect variatio n . k 
y
x
Holt Algebra 1
 4.
5-5
Direct Variation
The value of y varies directly with x, and y = 3,
when x = 9. Find y when x = 21.
y

x
3
9
y7
Holt Algebra 1
y

3
21 9
9 y  63
5-5
Direct Variation
y  2x
distance (mi)
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.
y
12
9
6
3
1 2
3 4
time (h)
Holt Algebra 1
5
x
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.
P x  4x
x
P x
x
x
Perimeter
20
15
10
5
x
HW pp. TBD
Holt Algebra 1
1 2
3 4
side length
5
x
5-5
Direct Variation
Learning Targets
Write a linear equation in slope-intercept form.
Graph a line using slope-intercept form.
Holt Algebra 1
5-5
Direct Variation
Graph the line given the slope and y-intercept.
y intercept = 4

R ISE
RUN

2
y
5
2
5
Holt Algebra 1
x
5-5
Direct Variation
Graph the line given the slope and y-intercept.
slope = 4; y-intercept =

R ISE
RUN

y
4
1
1
4
x
Holt Algebra 1
5-5
Direct Variation
Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3

R ISE
RUN

y
2
1
1
2
Holt Algebra 1
x
5-5
Direct Variation
Graph the line given the slope and y-intercept.
slope =

R ISE
RUN
, y-intercept = 1

y
2
3
2
3
Holt Algebra 1
x
5-5
Direct Variation
Write the equation that describes the line in
slope-intercept form.
slope =
; y-intercept = 4
y  mx  b
y 
1
4
Holt Algebra 1
x4
5-5
Direct Variation
Write the equation that describes the line in
slope-intercept form.
slope = –9; y-intercept =
y  mx  b
y  9 x 
5
4
Holt Algebra 1
5-5
Direct Variation
Write the equation that describes the line in
slope-intercept form.
slope = 2; (3, 4) is on the line
y  mx  b
4  2 3  b
46b
6 6
2  b
y  2x  2
Holt Algebra 1
5-5
Direct Variation
Graph the line described by the equation.
y = 3x – 1

R ISE
RUN

y
3
1
1
3
Holt Algebra 1
x
5-5
Direct Variation
Graph the line described by the equation.
2y + 3x = 6
y
3x 3x
2 y  3 x  6
2
y
2
2
3
x3
2

R ISE
RUN
Holt Algebra 1

3
2
3
2
x
5-5
Direct Variation
HW pp. 329/10-34 even & pp. 338-340/13-29,31
Graph the line described by the equation.
y = –4
y
y  mx  b
y  0x  4
x
Holt Algebra 1