learn to recognize direct variation by graphing tables of data and checking for constant ratios
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 PresentationTRANSCRIPT
![Page 1: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/1.jpg)
Pre-Algebra
11-5 Direct Variation
Learn to recognize direct variation by graphing tables of data and checking for constant ratios.
![Page 2: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/2.jpg)
Pre-Algebra
11-5 Direct Variation
![Page 3: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/3.jpg)
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
![Page 4: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/4.jpg)
Pre-Algebra
11-5 Direct Variation
Determine whether the data set shows direct variation.
A.
Example 1: Determining Whether a Data Set Varies Directly
![Page 5: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/5.jpg)
Pre-Algebra
11-5 Direct Variation
Make a graph that shows the relationship between Adam’s age and his length.
Example 1 Continued
![Page 6: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/6.jpg)
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
![Page 7: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/7.jpg)
Pre-Algebra
11-5 Direct Variation
Determine whether the data set shows direct variation.
B.
Example 2: Determining Whether a Data Set Varies Directly
![Page 8: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/8.jpg)
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.
![Page 9: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/9.jpg)
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
![Page 10: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/10.jpg)
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
![Page 11: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/11.jpg)
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
![Page 12: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/12.jpg)
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.
![Page 13: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/13.jpg)
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
![Page 14: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/14.jpg)
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.
![Page 15: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/15.jpg)
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
![Page 16: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/16.jpg)
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
![Page 17: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/17.jpg)
Pre-Algebra
11-5 Direct Variation
4. x is 12 when y is 15
Example 4: Finding Equations of Direct Variation
y = kx
.
![Page 18: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/18.jpg)
Pre-Algebra
11-5 Direct Variation
5. y is 8 when x is 5
Example 5: Finding Equations of Direct Variation
![Page 19: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/19.jpg)
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
![Page 20: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/20.jpg)
Pre-Algebra
11-5 Direct Variation
B. x is 28 when y is 14
Example 9
![Page 21: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/21.jpg)
Pre-Algebra
11-5 Direct Variation
C. y is 7 when x is 3
Example 10
![Page 22: Learn to recognize direct variation by graphing tables of data and checking for constant ratios](https://reader035.vdocuments.net/reader035/viewer/2022062407/56812b97550346895d8fb837/html5/thumbnails/22.jpg)
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