Скачать презентацию Algebra 4 5 Direct Variation Direct Variation Скачать презентацию Algebra 4 5 Direct Variation Direct Variation

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Algebra 4. 5 Direct Variation Algebra 4. 5 Direct Variation

Direct Variation Model The two variables x and y are said to vary directly Direct Variation Model The two variables x and y are said to vary directly if their relationship is: y = kx k is the same as m (slope) k is called the constant of variation

The price of hot dogs varies directly with the number of hotdogs you buy The price of hot dogs varies directly with the number of hotdogs you buy You buy hotdogs. x represents the number of hotdogs you buy. y represents the price you pay. y = kx 21 = k(7) 7 7 Let’s figure out k, the price per hotdog. Suppose that when you buy 7 hotdogs, it costs $21. Plug that information into the model to solve for k. Now divide both sides by 7 to solve for k. k=3 The price per hotdog is $3. y = 3 x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

y The graph of y = 3 x goes through the origin. All direct y The graph of y = 3 x goes through the origin. All direct variation graphs go through the origin, because when x = 0, y= 0 also. x

y (price) y = 3 x . . (3, 9) When you buy 3 y (price) y = 3 x . . (3, 9) When you buy 3 hotdogs, you pay $9 (2, 6) When you buy 2 hotdogs, you pay $6 (1, 3) When you buy 1 hotdog, you pay $3 x (number of hotdogs) (0, 0) When you buy 0 hotdogs, you pay $0

Finding the Constant of Variation (k) STEPS 1. Plug in the known values for Finding the Constant of Variation (k) STEPS 1. Plug in the known values for x and y into the model: y = kx 2. Solve for k 3. Now write the model y = kx and replace k with the number 4. Use the model to find y for other values of x if needed

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10.

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10. 1.

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10. 1.

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10. 1.

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10. 1. 2.

Example The variables x and y vary directly. When x = 24, y = Example The variables x and y vary directly. When x = 24, y = 84. 1. Write the direct variation model that relates x and y. 2. Find y when x is 10. 1. 2. When x = 10, y = 35

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1. 2.

Example The variables x and y vary directly. When x = ½, y = Example The variables x and y vary directly. When x = ½, y = 18. 1. Write the direct variation model that relates x and y. 2. Find y when x is 5. 1. 2. When x = 5, y = 180

Homework Pg. 238 #23 -31, 38 -41 Homework Pg. 238 #23 -31, 38 -41