Embed Size (px)
DESCRIPTION
Learn to recognize direct variation by graphing tables of data and checking for constant ratios. 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. - PowerPoint PPT Presentation
Citation preview
Pre-Algebra
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
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.
Helpful Hint
Pre-Algebra
11-5 Direct Variation
Determine whether the data set shows direct variation.
A.
Example 1: Determining Whether a Data Set Varies Directly
Pre-Algebra
11-5 Direct Variation
Make a graph that shows the relationship between Adam’s age and his length.
Example 1 Continued
Pre-Algebra
11-5 Direct Variation
You can also compare ratios to see if a direct variation occurs.
223
2712=
?81
264
81 ≠ 264
The ratios are not proportional.
The relationship of the data is not a direct variation.
Example 1 Continued
Pre-Algebra
11-5 Direct Variation
Determine whether the data set shows direct variation.
B.
Example 2: Determining Whether a Data Set Varies Directly
Pre-Algebra
11-5 Direct Variation
Make a graph that shows the relationship between the number of minutes and the distance the train travels.
Example 2 Continued
Plot the points.
The points lie in a straight line.
(0, 0) is included.
Pre-Algebra
11-5 Direct Variation
You can also compare ratios to see if a direct variation occurs.
The ratios are proportional. The relationship is a direct variation.
2510
5020
7530
10040= = = Compare ratios.
Example 2 Continued
Pre-Algebra
11-5 Direct Variation
Determine whether the data set shows direct variation.
A.
Example 3
Kyle's Basketball Shots
Distance (ft) 20 30 40
Number of Baskets 5 3 0
Pre-Algebra
11-5 Direct Variation
Make a graph that shows the relationship between number of baskets and distance.
Example 3 Continued
Num
ber
of
Bask
ets
Distance (ft)
2
3
4
20 30 40
1
5
Pre-Algebra
11-5 Direct Variation
You can also compare ratios to see if a direct variation occurs.
Example 3 Continued
520
330=
?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
Determine whether the data set shows direct variation.
B.
Example 4
Ounces in a Cup
Ounces (oz) 8 16 24 32
Cup (c) 1 2 3 4
Pre-Algebra
11-5 Direct Variation
Make a graph that shows the relationship between ounces and cups.
Example 4 Continued
Num
ber
of
Cup
s
Number of Ounces
2
3
4
8 16 24
1
32
Plot the points.
The points lie in a straight line.
(0, 0) is included.
Pre-Algebra
11-5 Direct Variation
You can also compare ratios to see if a direct variation occurs.
Example 4 Continued
The ratios are proportional. The relationship is a direct variation.
Compare ratios. = 1 8 = =2
163
24 432
Pre-Algebra
11-5 Direct Variation
Find each equation of direct variation, given that y varies directly with x.
3. y is 54 when x is 6
Example 3: Finding Equations of Direct Variation
Pre-Algebra
11-5 Direct Variation
4. x is 12 when y is 15
Example 4: Finding Equations of Direct Variation
y = kx
.
Pre-Algebra
11-5 Direct Variation
5. y is 8 when x is 5
Example 5: Finding Equations of Direct Variation
Pre-Algebra
11-5 Direct Variation
Find each equation of direct variation, given that y varies directly with x.
6. y is 24 when x is 4
Example 6
Pre-Algebra
11-5 Direct Variation
B. x is 28 when y is 14
Example 9
Pre-Algebra
11-5 Direct Variation
C. y is 7 when x is 3
Example 10
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.
y = 26x
y = x19
y = x65
