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2.3 Direct Variation September 17, 2008 2.3 Direct Variation Objective Write and interpret direct variation equations. Old paper 1 2.3 Direct Variation September 17, 2008 Check Skills You'll Need: Solve each equation for y: 1. 12y = 3x 2. 12y = 5x 3. (3/4)y = 15 4. 0.9y = 27x Tell whether each equation is true: 5. 1 4 = 2 8 6. 2 5 = 6 15 7. 9 24 = 12 36 8. 20 24 = 30 36 Jul 31­8:41 AM 2 2.3 Direct Variation September 17, 2008 A DIRECT VARIATION is a line that always goes through the origin. y = mx + b slope What will ALWAYS be the value of b? y­intercept Jul 31­9:02 AM 3 2.3 Direct Variation September 17, 2008 The general form of a direct variation is y = kx k is the variation constant How do we find k? y = kx Divide both sides by x. y k= x Jul 31­9:14 AM 4 2.3 Direct Variation September 17, 2008 For the following function, does y vary directly with x? If so, find the constant of variation and write the equation. x y 2 8 3 12 5 20 k=4 y = 4x Jul 31­9:36 AM 5 2.3 Direct Variation September 17, 2008 For the following function, does y vary directly with x? If so, find the constant of variation and write the equation. x y 1 4 2 7 5 16 y/x is not constant y does not vary directly with x Jul 31­9:43 AM 6 2.3 Direct Variation September 17, 2008 Can you identify a direct variation from an equation? For each function, determine whether y varies directly with x. If so, find the constant of variation. a. 3y = 2x b. y = 2x + 3 y = (2/3)x k = 2/3 not direct variation Jul 31­9:47 AM 7 2.3 Direct Variation September 17, 2008 A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. Find the constant of variation k and write an equation to model the direct variation. Step 1: What is the problem asking us? water wasted varies directly with time Step 2: Define variables. Let w = # of cups wasted Let t = time in minutes the faucet drips Step 3: Write an equation. w = kt 1 = k(3) 1/3 = k Substitute 1 for w and 3 for t. Step 4: Write the direct variation equation with k. w = (1/3)t Jul 31­10:25 AM 8 2.3 Direct Variation September 17, 2008 y varies directly with x x = 27 and y = -51 Find x when y = -17 Step 1: Set up a proportion y1 y2 = x1 x2 Step 2: Plug in the numbers. ­51 ­17 = x2 27 Step 3: Simplify. x2 = 9 Jul 31­11:21 AM 9 2.3 Direct Variation September 17, 2008 HOMEWORK p. 74 #1 ­ 27, 52 Old paper 10