CHAPTER 1.4, DATE_______. DIRECT VARIATION 1. Line through the origin 2. y varies directly as x (as x changes so will y at a constant rate, k) y = kx.

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Presentation transcript:

CHAPTER 1.4, DATE_______

DIRECT VARIATION 1. Line through the origin 2. y varies directly as x (as x changes so will y at a constant rate, k) y = kx 3. k is called the “constant of variation”

Find the constant of variation, k, and the direct variation equation if y varies directly as x and y = -24 when x = 4 1 st plug given into formula and solve for k (y=kx) -24 = k(4) 4 -6 = k 2 nd rewrite equation with the constant (k) y = -6x

Find the constant of variation, k, and the direct variation equation if y varies directly as x and y = 5 when x = st plug given into formula and solve for k (y=kx) 5 = k(-0.1) = k 2 nd rewrite equation with the constant (k) y = -50x

If the table represents a direct variation, write an equation for the variation. XY st – divide y by x 2 nd -does it stay consistent? 3 rd -write it in direct variation 4 yes y = 4x

If the table represents a direct variation, write an equation for the variation. XY st – Divide y by x 2 nd -does it stay consistent? 3 rd -write it in direct variation no Can’t

Cross Product Property of Proportions a c b d = IF Then ad = bc

Solve using the cross product property x x 40 = w = 40(x+1) = 45x 12w = W = 3.33 Ex 1. Ex 2. 40x + 40 = 45x -40x 40 = 5x 5 x = 8

Find the cost of 8 pairs of socks if 3 pairs of socks cost $ st – set up a comparison of the given information. socks $ 2 nd - plug in what you know-staying consistent with tops and bottoms 3 $ x = 3 rd – cross multiply and solve. 3x = 55.2 x = $18.40

Find the cost of 7 apples if 4 apples cost cost $ st – set up a comparison of the given information. apples $ 2 nd - plug in what you know-staying consistent with tops and bottoms 4 $ x = 3 rd – cross multiply and solve. 4x = x = $7.88