1 / 17

Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations.

Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations. Key Words: direct variation constant of variation. Direct Variation: Two variables x and y show direct variation , or vary directly , if y = kx

jasmine-kaufman
Download Presentation

Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations.

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. Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations. Key Words: direct variation constant of variation

  2. Direct Variation: Two variables x and y show direct variation, or vary directly, if y = kx where k is a nonzero constant called the constant of variation.

  3. Do you notice a direct variation?

  4. Example 1 y = x SOLUTION 7 7 Plot a point at the origin. 4 4 Write equation. y = x 7 ( ) Substitute 4 for x. 4 y = 4 Graph a Direct Variation Equation Graph . Find a second point by substituting a convenient value for x.

  5. Example 1 A second point is . ( 4, 7 ) y = 7 Graph a Direct Variation Equation Simplify. Plot the second point. Then draw a line through the two points as shown.

  6. Checkpoint ANSWER – 1. x y = ANSWER 2. 2 y x = Graph a Direct Variation Equation Graph the equation.

  7. Checkpoint ANSWER – 3. y 4x = ANSWER 2 4. y x = 3 Graph a Direct Variation Equation Graph the equation.

  8. Example 2 Write a Direct Variation Equation Recipes:To make mango salsa, replace the tomatoes in the recipe above with mangoes, using 3 mangoes for 2 recipes. Write an equation relating the number of servings y to the number of mangoes x given so that y varies directly with x. How many servings of salsa can you make if you have 5 mangoes?

  9. SOLUTION In 2 recipes there are servings, so 3 mangoes make 8 servings. This means when . Write an equation using these values of y and x to solve for k. ( ) 2 4 8 = y 8 x 3 = = Write a direct variation equation. y kx = ( ) Substitute 8 for y and 3 for x. k 3 8 = 8 Simplify. k = 3 8 An equation is . To find how many servings of salsa you can make using 5 mangoes, substitute 5 for x. y x = 3 Example 2 Write a Direct Variation Equation

  10. Example 2 ANSWER Five mangoes will make about 13 servings. Write a Direct Variation Equation 40 1 8 8 ( ) 13 y x 5 = = = = 3 3 3 3

  11. Checkpoint ANSWER 6. ANSWER 1 y x = 5 x 10, y 2 = = x 3, y y – – 9 3x = = = Write a Direct Variation Equation The variables x and y vary directly. Write an equation that relates x and y. 5.

  12. CHEFS create dishes and menus that will appeal to their customers. Executive chefs supervise kitchen operations and food service staff.

  13. Lines, x 5 10 15 20 25 Words, y 153 305 454 602 757 SOLUTION Find the ratio of y to x for each data pair. 454 757 30.28 30.27 ≈ ≈ 153 305 602 15 25 30.6 30.1 30.5 = = = 5 20 10 Example 3 Identify Direct Variation Tell whether the data, the numbers of words y in the first x lines of the Declaration of Independence, show direct variation. If so, write an equation relating x and y.

  14. Example 3 Identify Direct Variation The ratio of y to x in each pair is nearly the same, so the data show direct variation. Substituting 30.3 for k in ykx gives the direct variation equation y30.3x. = =

  15. Checkpoint 7. Tell whether the data show direct variation. If so, write an equation relating x and y. not direct variation ANSWER ( ), ( ), ( ), ( ), ( ) 1, 2 2, 4 3, 8 4, 14 5, 22 Identify Direct Variation

  16. Slip

  17. Homework

More Related