Learn to recognize direct variation by graphing tables of data and checking for constant ratios.

1. Learn to recognize direct variation by graphing tables of data and checking for constant ratios.

3. 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.

4. Example 1: Determining Whether a Data Set Varies Directly Determine whether the data set shows direct variation. A.

5. Example 1 Continued Make a graph that shows the relationship between Adam’s age and his length.

6. 27 22 12 3 ? = Example 1 Continued You can also compare ratios to see if a direct variation occurs. 81 81 ≠ 264 The ratios are not proportional. 264 The relationship of the data is not a direct variation.

7. Example 2: Determining Whether a Data Set Varies Directly Determine whether the data set shows direct variation. B.

8. 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.

9. 25 10 75 100 50 30 40 20 Example 2 Continued You can also compare ratios to see if a direct variation occurs. Compare ratios. = = = The ratios are proportional. The relationship is a direct variation.

10. Example 3 Determine whether the data set shows direct variation. A.

11. Example 3 Continued Make a graph that shows the relationship between number of baskets and distance. 5 4 3 Number of Baskets 2 1 20 30 40 Distance (ft)

12. 3 5 30 20 ? = Example 3 Continued You can also compare ratios to see if a direct variation occurs. 60 150  60. The ratios are not proportional. 150 The relationship of the data is not a direct variation.

13. Example 4 Determine whether the data set shows direct variation. B.

14. 4 3 Number of Cups 2 1 32 8 16 24 Number of Ounces Example 4 Continued Make a graph that shows the relationship between ounces and cups. Plot the points. The points lie in a straight line. (0, 0) is included.

15. 1 = = = 8 3 4 2 24 32 16 Example 4 Continued You can also compare ratios to see if a direct variation occurs. Compare ratios. The ratios are proportional. The relationship is a direct variation.

16. 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

17. Example 4: Finding Equations of Direct Variation 4. x is 12 when y is 15 y = kx .

18. Example 5: Finding Equations of Direct Variation 5. y is 8 when x is 5

19. Example 6 Find each equation of direct variation, given that y varies directly with x. 6. y is 24 when x is 4

20. Example 9 B. x is 28 when y is 14

21. Example 10 C. y is 7 when x is 3

22. y = x y = x 1 6 9 5 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