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Direct variation is a linear relationship while inverse variation is an inverse relationship. Always a line through the origin. 1. Joint Variation – when a quantity varies directly as a product of 2 or more other quantities. The equation would be something like y kxz which would be “y varies jointly as x and z.” 2.
Determine whether each situation is an example of a direct variation or inverse variation. Write and equations of variation to represent the situation and solve for the indicated information.
Tell whether x and y show direct variation, inverse variation, or neither. 6. 7) If y varies directly to x, and y = 6 when x = 15, find y when x = 25. 8) If y varies inversely to x, and y = 9 when x = 6, find y when x = 3. 9) If p varies jointly to q and t, and p = 9 when q = 3 and t = 1, find q when p = 24 and t=3.
Direct Variation:y = kx The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for five attendees was $100. How much money will be raised for 60 attendees?
Joint Variation ! Describes situations where y increases as x and z increase (direct variation but with two or more variables). ! For example – The formula for the area of a triangle is A = ½bh. The area varies “jointly” with the length of the base and the height.
Direct and Inverse Variation Worksheet Name:_____ Find the Missing Variable: 1) y varies directly with x. If y = -4 when x = 2, find y when x = -6. 2) y varies inversely with x. If y = 40 when x = 16, find x when y = -5. 3) y varies inversely with x. If y = 7 when x = -4, find y when x = 5. 4) y varies directly with x.
9.1 Direct, Inverse, Joint, and Combined Variation RECALL from Algebra 1: Direct Variation If y varies directly as x, then y = kx. Example 1 The variable y varies directly as x, and y = 6 when x = 2. a)Find the constant of variation. b)Write the appropriate inverse variation equation.
