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Solve for a .

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. 2 a. =. 5. ANSWER. 5 to 8. 16. –. 2. –. ANSWER. 5 a. =. 16. 5. 3.

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Solve for a .

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  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

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