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3-4 Direct Variation

3-4 Direct Variation. Goal: Write linear equations that represent direct variation. Vocabulary. Direct Variation - When two variables are related in such a way that the ratio of their values always remains the same. Constant of Variation – the relationship between the two variables.

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3-4 Direct Variation

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  1. 3-4 Direct Variation Goal: Write linear equations that represent direct variation

  2. Vocabulary Direct Variation - When two variables are related in such a way that the ratio of their values always remains the same. Constant of Variation – the relationship between the two variables

  3. In other words : • Direct variation is when one variable is a multiple of the other variable. • Equation looks like: y = kx • k can be any number except 0. • We call k the constant of variation.

  4. Example • If a gallon of milk costs $2, and I buy 1 gallon, the total cost is $2. If I buy 10 gallons, the price is $20. • In this example the total cost of milk and the number of gallons purchased are subject to direct variation -- the ratio of the cost to the number of gallons is always 2. • So the equation would be y = 2x • y is the cost and x is the number of gallons of milk. • 2 is the constant of variation.

  5. Graphical Interpretation • If y varies directly as x, then the graph of all points that describe this relationship is a line going through the origin (0, 0) whose slope is called the constant of the variation. • If we graph the equation y = kx • The y-intercept is 0 • The slope is k (the constant of variation)

  6. Examples Find the constant of variation and the slope of each direct variation problem. 1. y = 2x 2. y = - ½ x m = - ½ k = - ½ m = 2 k = 2

  7. A.constant of variation: 4; slope: –4 B.constant of variation: 4; slope: 4 C. constant of variation: –4; slope: –4 D.constant of variation: slope: Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

  8. A.constant of variation: 3; slope: 3 B.constant of variation: slope: C. constant of variation: 0; slope: 0 D.constant of variation: –3; slope: –3 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

  9. Examples The variables x and y vary directly. Use the given values to write an equation that relates x and y. x = 5 and y = 20 x = -3 and y = -30 x = 10 and y = 5 x = 35 and y = 7 x = 17 and y = 4.25 y = 4x y = 10x y = ½ x y = 1/5 x y = ¼ x

  10. Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates xand y. A.y = 3x B.y = 15x C.y = 5x D.y = 45x

  11. Practice • Worksheet – “3-4Direct Variation” • Complete part A

  12. More Examples Assume the variables vary directly. Use an equation to find the value of y. If x = 4 when y = 12, find y when x = -2. If x = 1 when y = -7, find y when x = 3. If x = 12 when y = 2, find y when x = 18. If x = 3 when y = 36, find y when x = -4. y = -6 y = -21 y = 3 y = -48

  13. Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find xwhen y= –45. A. –3 B. 9 C. –15 D. –5

  14. More Practice • Worksheet – “3-4Direct Variation” • Complete part B

  15. Homework Pages 185-186 #10-15 #24-27

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