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5.2 direct variation Write and graph a direct variation equation. 5.2 Getting ready The time it takes to hear thunder varies directly with the distance from the lightning. Direct Variation: A function represented by the equation: y = kx where k≠ 0 a. The coefficient of x. Constant of variation: b. 𝑘 = 𝑦 𝑥 Determine whether each equation represents a direct variation? If so, find the constant of variation. B). 3y + 4x = 8 -4x - 4x A). 7y = 2x 7 7 3y 3 y = 2x 7 Is the equation in the form of y = kx? yes The constant of variation is: Or k = 2 7 2 7 = 8 - 4x 3 3 y = 8 – 4x 3 3 Is the equation in the form of y = kx? No, so it’s not a direct variation. Suppose y varies directly with x, and y = 35 when x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9? Direction variation equation form: Solve for k: Use y = 35 and x = 5 Write your new equation: What is the value of y when x = 9? (substitute and solve) y = kx 35 = k(5) 7=k y = 7x y = 7x y = 7(9) y = 63 Weight on Mars y varies directly with weight on Earth x. The weights of the science instruments onboard the Phoenix Mars Lander weigh 50 lbs on Mars and 130 lbs on Earth. What is an equation that relates weight, in pounds, on Earth x and weight on Mars y? y = kx 50 = k(130) .38 = k Solve for k: Substitute x = 130 y = 50 y = .38x Make a table and graph the equation. x 0 50 100 150 y 0 19 38 57 Graphs of direct variations: 1. Equation: y= kx 2. Line passes through (0,0) 3. The slope of the line = k. k>0 k<0 Does y vary directly with x? If it does, write an equation for the direct variation. How? x 4 8 10 y 6 12 15 Find k 𝑦 𝑥 6 = 4 x 1.5 12 = 8 1.5 15 = 10 1.5 Yes. It is a direct variation equation because the ratio 𝑦 is the same. 𝑥 y = 1.5x y -2 1 4 3.2 2.4 1.6 𝑦 𝑥 3.2 = −2 -1.6 2.4 = 1 2.4 1.6 = 4 .4 No. It isn’t a direct variation equation because the ratio 𝑦 isn′ t the same. 𝑥 Assignment: pg 304 10-38 even.