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Direct variation describes a relationship where one variable (y) changes directly as another variable (x) changes, expressed as y = kx, where k is a constant. When x increases, y increases, and when x decreases, y decreases. The graph of a direct variation always passes through the origin (0,0) and the constant k can be either positive or negative (but never zero). To determine if a relationship represents direct variation, rearrange the equation to the form y = kx and solve for k. Explore examples and practice problems to enhance your understanding.
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Definition: Y varies directly as x means that y = kx where k is the constant of variation. (see any similarities to y = mx + b?) Another way of writing this is k = In other words: * As X increases in value, Y increases or * As X decreases in value, Y decreases.
Direct Variation: y = kx • y varies directly with x • y varies directly as x • k = constant of variation = slope • The graph of a direct variation ALWAYS goes through (0,0), the origin • K is never 0. • K can be positive or negative.
Direct Variation or not? • Solve for y • Put the equation in the form y = kx • Does y vary directly with x? If so, find k. • 2x – 3y = 1 • 2x – 3y = 0
3. ½ x + 1/3y = 0 • 4. 7y = 2x • 5. 3y + 4x = 8
Tell if the following graph is a Direct Variation or not. Yes No No No
Tell if the following graph is a Direct Variation or not. Yes No No Yes
Determine if each data table represents a direct variation. If so, write the equation.
Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 6/4 or 3/2 Equation? y = 3/2 x
Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!
Graph the Direct Variation Equation • y=3/2x.
One More Graph y =4x
Writing direct variation Equations • x = 3, y =9 • x=1/4, y=1
