2-3 notes - y varies directly with x . If so, find the...

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Section 2-3 Direct Variation Warm-up: Solve each equation for y 1) x y 3 12 = 2) x y 15 4 3 = 3) y x 9 . 0 27 = Objectives: 1 – Identify direct variation 2 – Find the constant of variation and write direct variation equations What do you notice about the values in this table? Are there any patterns? This table represents a special kind of relationship called direct variation. A linear equation of the form y = kx , where k = 0, represents direct variation . These equations can be written as so the ratio y : x equals the constant k . We call k the _____________________. Example 1) For the following functions, determine if y varies directly with x . If so, find the constant of variation and write the equation. x y -6 -2 3 1 12 4
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x y 1 4 2 7 5 16 If we graphed the equation we wrote for part a, what would it look like? Example 2) For each of the following, determine if
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Unformatted text preview: y varies directly with x . If so, find the constant of variation. a. x y 2 3 = b. 10 4 7 = + y x c) 4 x y = Example 3) Writing a direct variation equation. A dripping faucet wastes one cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. a. Find the constant of variation, and write an equation to model the situation. b. How long would it take to waste 4 cups of water? You can also use a proportion to solve in direct variation situations. Example 4) a. Suppose y varies directly with x , and if y = 4 then x = 3. Find y when x = 6. b. Suppose y varies directly with x , and if y = 10 then x = -3. Find y when x = 2....
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2-3 notes - y varies directly with x . If so, find the...

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