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2.3 Direct Variation Objective Write and interpret direct variation equations. Title: Old paper (1 of 12) 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. Title: Jul 31­8:41 AM (2 of 12) 2 5 = 6 15 7. 9 24 = 12 36 8. 20 24 = 30 36 A DIRECT VARIATION is a line that always goes through the origin. y = mx + b slope Title: Jul 31­9:02 AM (3 of 12) y­intercept What will ALWAYS be the value of b? The general form of a direct variation is y = kx k is the variation constant How do we find k? y = kx y k= x Title: Jul 31­9:14 AM (4 of 12) Divide both sides by x. 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 ANSWER y = 4x Title: Jul 31­9:36 AM (5 of 12) 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 ANSWER y does not vary directly with x Title: Jul 31­9:43 AM (6 of 12) 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 y = (2/3)x k = 2/3 Title: Jul 31­9:47 AM (7 of 12) b. y = 2x + 3 not direct variation 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 Title: Jul 31­10:25 AM (8 of 12) 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. ANSWER x2 = 9 Title: Jul 31­11:21 AM (9 of 12) HOMEWORK p. 74 #1 ­ 22, 52, 55­58 Title: Old paper (10 of 12) Title: Sep 17­10:29 AM (11 of 12) Find the equation of the line through the points (­6, 4) and (­3, 6). Write the equation in all three forms Find the equation of the line perpendicular to 3x ­ 5y = ­7 and through the point (­6, ­2). Title: Sep 17­12:39 PM (12 of 12)