1 / 12

Understanding Direct Variation: Flower Ratios, Equations & Mango Salsa Recipe

This lesson explores the concept of direct variation through various examples, including finding the ratio of a flower's width to a leaf's length, plotting points on a graph, and writing equations that represent relationships between variables. The curriculum also includes an engaging recipe activity, replacing tomatoes with mangoes to illustrate how to write equations in direct variation related to servings. Key exercises reinforce understanding of variables and direct relationships, making connections between math and real-life applications.

herman-stout
Download Presentation

Understanding Direct Variation: Flower Ratios, Equations & Mango Salsa Recipe

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. 4. A flower is 4.5 centimeters wide and has a leaf 7.2 centimeters long. What is the ratio of flower width to leaf length? 1. ANSWER 10 2a = 5 ANSWER 5to8 16 – 2. – ANSWER 5a = 16 5 3. Write an equation of the line that passes through the points and . ( ) ( ) 4, 8 0, 0 ANSWER y = 2x Warm-Up Exercises Solve for a.

  2. 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.

  3. 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.

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

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

  6. 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?

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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. = =

  12. 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

More Related