11-5 Direct Variation
Learn to recognize direct variation by graphing
tables of data and checking for constant ratios.
Pre-Algebra
11-5 Direct Variation
Pre-Algebra
11-5 Direct Variation
Helpful Hint
The graph of a direct-variation equation is always
linear and always contains the point (0, 0). The
variables x and y either increase together or
decrease together.
Pre-Algebra
11-5 Direct Variation
Example 1: Determining Whether a Data Set Varies
Directly
Determine whether the data set shows direct
variation.
A.
Pre-Algebra
11-5 Direct Variation
Example 1 Continued
Make a graph that shows the relationship between
Adam’s age and his length.
Pre-Algebra
11-5 Direct Variation
Example 1 Continued
You can also compare ratios to see if a direct
variation occurs.
22 ? 27
3 = 12
81 81 ≠ 264
264
The ratios are not proportional.
The relationship of the data is not a direct
variation.
Pre-Algebra
11-5 Direct Variation
Example 2: Determining Whether a Data Set Varies
Directly
Determine whether the data set shows direct
variation.
B.
Pre-Algebra
11-5 Direct Variation
Example 2 Continued
Make a graph that shows the relationship between
the number of minutes and the distance the train
travels.
Plot the points.
The points lie in
a straight line.
(0, 0) is included.
Pre-Algebra
11-5 Direct Variation
Example 2 Continued
You can also compare ratios to see if a direct
variation occurs.
25 = 50= 75 = 100
10 20 30 40
Compare ratios.
The ratios are proportional. The relationship is
a direct variation.
Pre-Algebra
11-5 Direct Variation
Example 3
Determine whether the data set shows direct
variation.
A.
Kyle's Basketball Shots
Distance (ft)
Number of Baskets
Pre-Algebra
20
30
40
5
3
0
11-5 Direct Variation
Example 3 Continued
Make a graph that shows the relationship between
number of baskets and distance.
Number of Baskets
5
4
3
2
1
20 30 40
Distance (ft)
Pre-Algebra
11-5 Direct Variation
Example 3 Continued
You can also compare ratios to see if a direct
variation occurs.
5 ? 3
20= 30
60
150
150  60.
The ratios are not proportional.
The relationship of the data is not a direct
variation.
Pre-Algebra
11-5 Direct Variation
Example 4
Determine whether the data set shows direct
variation.
B.
Ounces in a Cup
Ounces (oz)
8
16
24
32
Cup (c)
1
2
3
4
Pre-Algebra
11-5 Direct Variation
Example 4 Continued
Number of Cups
Make a graph that shows the relationship between
ounces and cups.
Plot the points.
4
3
The points lie in
a straight line.
2
(0, 0) is included.
1
8
16 24 32
Number of Ounces
Pre-Algebra
11-5 Direct Variation
Example 4 Continued
You can also compare ratios to see if a direct
variation occurs.
1= 2 = 3 = 4
8 16 24 32
Compare ratios.
The ratios are proportional. The relationship is
a direct variation.
Pre-Algebra
11-5 Direct Variation
Example 3: Finding Equations of Direct Variation
Find each equation of direct variation, given
that y varies directly with x.
3. y is 54 when x is 6
Pre-Algebra
11-5 Direct Variation
Example 4: Finding Equations of Direct Variation
4. x is 12 when y is 15
y = kx
.
Pre-Algebra
11-5 Direct Variation
Example 5: Finding Equations of Direct Variation
5. y is 8 when x is 5
Pre-Algebra
11-5 Direct Variation
Example 6
Find each equation of direct variation, given
that y varies directly with x.
6. y is 24 when x is 4
Pre-Algebra
11-5 Direct Variation
Example 9
B. x is 28 when y is 14
Pre-Algebra
11-5 Direct Variation
Example 10
C. y is 7 when x is 3
Pre-Algebra
11-5 Direct Variation
Lesson Review: Part 1
Find each equation of direct variation, given
that y varies directly with x.
1. y is 78 when x is 3.
2. x is 45 when y is 5.
3. y is 6 when x is 5.
Pre-Algebra
y = 26x
y =1 x
9
y =6 x
5