Section 2-3 Direct VariationWarm-up: Solve each equation for y1) xy312=2) xy1543=3) yx9.027=Objectives:1 – Identify direct variation2 – Find the constant of variation and write direct variation equationsWhat do you notice about the values in this table? Are there any patterns?k.Example 1) For the following functions, determine if yvaries directly with x. If so, find the constant of variation and write the equation. xy-6-231124
xy1427516If we graphed the equation we wrote for part a, what would it look like?Example 2) For each of the following, determine if yvaries directly with x. If so, find the constant of variation. a. xy23=b. 1047=+yxc) xy=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 4½ cups of water? 4
You can also use a proportion to solve in direct variation situations. Example 4) a. Suppose yvaries directly with x, and if y= 4 then xFind ywhen x= 6. b. Suppose yvaries directly with x, and if y= 10 then xFind ywhen x= 2. = 3. = -3.