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Understanding Direct Variation: Equations and Examples

This guide explains direct variation, emphasizing how to set up direct variation equations using the formula y = kx, where k is the constant of variation. It illustrates the concept with practical examples involving costs of soft drinks, gasoline, and worker earnings, detailing the steps to identify the variation constant and formulate the specific equation. Readers will learn how to calculate costs based on varying quantities and understand the relationship between directly proportional variables in real-world scenarios.

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Understanding Direct Variation: Equations and Examples

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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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