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4.6 Direct Variations

4.6 Direct Variations. 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

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4.6 Direct Variations

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  1. 4.6 Direct Variations

  2. 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.

  3. 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.

  4. 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

  5. 3. ½ x + 1/3y = 0 • 4. 7y = 2x • 5. 3y + 4x = 8

  6. Tell if the following graph is a Direct Variation or not. Yes No No No

  7. Tell if the following graph is a Direct Variation or not. Yes No No Yes

  8. Determine if each data table represents a direct variation. If so, write the equation.

  9. 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

  10. Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!

  11. Graph the Direct Variation Equation • y=3/2x.

  12. One More Graph y =4x

  13. Writing direct variation Equations • x = 3, y =9 • x=1/4, y=1

  14. Classwork/Homework

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