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HN Math II

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

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HN Math II

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  1. HN Math II Direct Variation

  2. 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

  3. 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 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. y = kx 21 = k(7) Now divide both sides by 7 to solve for k. 7 7 k = 3 The price per hotdog is $3. y = 3x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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