Solve for a. Warm-Up Exercises 1. 2a2a10 = 2. 165a5a= – 3. Write an equation of the line that passes through the points and. ( ) 0, 0 ( ) 4, 8 ANSWER 5.

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Solve for a. Warm-Up Exercises 1. 2a2a10 = a5a= – 3. Write an equation of the line that passes through the points and. ( ) 0, 0 ( ) 4, 8 ANSWER – ANSWER 2x2xy= 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? ANSWER 5 to 8

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

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

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

Checkpoint Graph the equation. ANSWER Graph a Direct Variation Equation 4x4xy = – y x =

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?

Example 2 Write a Direct Variation Equation 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. SOLUTION () 42 8 = 8y = 3x = kxkxy = Write a direct variation equation. 8 = Substitute 8 for y and 3 for x. () 3k = Simplify. k 3 8 An equation is. To find how many servings of salsa you can make using 5 mangoes, substitute 5 for x. = x 3 8 y

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

Checkpoint The variables x and y vary directly. Write an equation that relates x and y. 5. x = 3,3, y = 9 – ANSWER y = 3x3x – 6. x = 10, y = 2 ANSWER = x 5 1 y Write a Direct Variation Equation

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. SOLUTION Find the ratio of y to x for each data pair = = = ≈ ≈ Words, y Lines, x

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 y kx gives the direct variation equation y 30.3x. ==

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