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Direct Variation

Direct Variation. Objective: to solve for k and set up a direct variation equation. Direct Variation. Constant : A value that does not change Example: 1.6 km per mile Directly proportional : two variables that have a constant ratio. Example: Direct variation : An equation in the form

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Direct Variation

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  1. Direct Variation Objective: to solve for k and set up a direct variation equation

  2. Direct Variation Constant: A value that does not change Example: 1.6 km per mile Directly proportional: two variables that have a constant ratio. Example: Direct variation: An equation in the form y = kx, kis the constant of variation and can be found when you take y and divide it by x. Example: y = 1.6x, where y is kilometers andx is miles.

  3. The cost of a soft drink varies directly with the number of ounces you buy. It costs $.96 for a 12 oz. bottle. The steps to follow to write a direct variation equation: 1. What is the generic formula for a direct variation equation? y = kx 2. What is the variation constant (k) for this problem? k = 0.08 3. What is the equation for this problem? (make it specific for this problem) c = kn, where c = cost and n = ounces c = .08n 4. How much does it cost to buy a 16 oz pop bottle? c = .08(16) c = $1.28 c = .08n

  4. The cost of gasoline varies directly with the number of gallons bought. It costs $33 to buy 12 gallons of gas. The steps to follow to write a direct variation equation: 1. What is the generic formula for a direct variation equation? y = kx or k = y/x 2. What is the variation constant (k) for this problem? k = 2.75 3. What is the equation for this problem? (make it specific for this problem) c = 2.75n c = kn, where c = cost and n= gallons bought 4. How much does it cost to buy 7.5 gallons of gas? c = 2.75(7.5) c = $20.63 c = 2.75n

  5. A worker earns $1010 in a 40 hour work week. The steps to follow to write a direct variation equation: Hours $ 1. What is the generic formula for a direct variation equation? $___ hours y = kx 2. What is the variation constant (k) for this problem? k = 25.25 3. What is the equation for this problem? (make it specific for this problem) m = 25.25h m = kh, where m = money earned and h = hours worked 4. How many hours did he work if he got paid $4848. 4848 = 25.25 (h) h = 192 m = 25.25h

  6. assignment • Direct variation worksheet 1-5

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