1 / 31

Direct Variation Exploration: Understanding Ratios & Graphs

Dive into direct variation in Course 3 with helpful hints, questions, examples, and quizzes. Learn to identify relationships through ratios, graphs, and origin. Practice plotting points and determining direct variation. Enhance your skills through engaging exercises.

sherryunderwood
Download Presentation

Direct Variation Exploration: Understanding Ratios & Graphs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Direct Variation

  2. Warm-Up Course 3 Insert Lesson Title Here

  3. Warm-Up Day 2 Course 3 Insert Lesson Title Here

  4. Direct Variation 12-5 Course 3 Insert Lesson Title Here Vocabulary

  5. Direct Variation 12-5 Helpful Hint • The graph of a direct-variation equation is always linear (straight line) • The graph of direct-variation equation always contains the origin (0, 0). • The variables x and y either increase together or decrease together. Course 3 Origin

  6. Direct Variation 12-5 Helpful Hint Course 3 Direct Variation - When the ratios are proportional the relationship is a direct variation.

  7. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation. X Y • QUESTIONS: • Do x and yboth increase or decrease? • Are the ratios proportional? • Is the graph a straight line? • Does the line pass through the origin?

  8. Direct Variation 12-5 Course 3 Additional Example 1B 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. Direct Variation 12-5 25 10 50 20 Course 3 Additional Example 1B Continued You can also compare ratios to see if a direct variation occurs. Compare ratios. = When the ratios are proportional. The relationship is a direct variation.

  10. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation. X y • QUESTIONS: • Do x and yboth increase or decrease? • Are the ratios proportional? • Is the graph a straight line? • Does the line pass through the origin?

  11. Direct Variation 12-5 Course 3 Check It Out: Example 1A Continued Make a graph that shows the relationship between number of baskets and distance. The graph is not linear. 5 4 3 Number of Baskets 2 1 20 30 40 Distance (ft)

  12. Direct Variation 12-5 3 5 30 20 ? = Course 3 Check It Out: Example 1A 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. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation.

  14. Direct Variation 12-5 Course 3 X y • QUESTIONS: • Do x and yboth increase or decrease? • Are the ratios proportional? • Is the graph a straight line? • Does the line pass through the origin?

  15. Direct Variation 12-5 Course 3 X y

  16. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation. • QUESTIONS: • Do x and yboth increase or decrease? • Are the ratios proportional? • Is the graph a straight line? • Does the line pass through the origin?

  17. Direct Variation 12-5 4 3 Number of Cups 2 1 32 8 16 24 Number of Ounces Course 3 Check It Out: Example 1B 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.

  18. Direct Variation 12-5 1 = = = 8 3 4 2 24 32 16 Course 3 Check It Out: Example 1B 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.

  19. Direct Variation 12-5 Course 3 Determine whether the graph shows direct variation.

  20. Direct Variation 12-5 Course 3 Determine whether the graph shows direct variation.

  21. Direct Variation 12-5 Course 3 Determine whether the graph shows direct variation.

  22. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation.

  23. Direct Variation 12-5 Course 3 Determine whether the data set shows direct variation.

  24. Direct Variation 12-5 Course 3 Ticket Out the Door What are the four questions you should ask when determining whether there is a direct variation?

  25. Direct Variation Day 2

  26. Direct Variation 12-5 Course 3 Insert Lesson Title Here Vocabulary

  27. Direct Variation 12-5 Course 3 Check It Out: Example 2A Y varies directly with X. Solve and write an equation when x is 4 when y is 24 y = kx y varies directly with x. 24 = k4 Substitute for x and y. 6 = k Solve for k. Substitute 6 for k in the original equation. y = 6x

  28. Direct Variation 12-5 = k Course 3 Check It Out: Example 2B Y varies directly with X. Solve and write an equation when x is 14 when y is 28 y = kx y varies directly with x. 28 = k14 Substitute for x and y. Solve for k. Rewrite equation.

  29. Direct Variation 12-5 Course 3 Additional Example 2A: Finding Equations of Direct Variation Find each equation of direct variation, given that y varies directly with x. y is 54 when x is 6 y = kx y varies directly with x. 54 = k6 Substitute for x and y. 9 = k Solve for k. Substitute 9 for k in the original equation. y = 9x

  30. Direct Variation 12-5 = k y = x Substitute for k in the original equation. 5 5 5 4 4 4 Course 3 Y varies directly with X. Solve when x is 12 when y is 15 y = kx y varies directly with x. 15 = k12 Substitute for x and y. Solve for k.

  31. Direct Variation 12-5 Course 3 Insert Lesson Title Here Lesson Quiz: Part II 4. The table shows the amount of money Bob makes for different amounts of time he works. Determine whether there is a direct variation between the two sets of data. If so, find the equation of direct variation. direct variation; y = 12x

More Related