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Direct Variation

4.6 3-9 odd, 12-22 even, 23-25, 29-34. Direct Variation. Grab ONE sheet of graph paper. Rate of Change. As previously shown, rate of change is most easily identified as the slope of a line connecting two points

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Direct Variation

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  1. 4.6 • 3-9 odd, 12-22 even, 23-25, 29-34 Direct Variation Grab ONE sheet of graph paper

  2. Rate of Change As previously shown, rate of change is most easily identified as the slope of a line connecting two points This concept aids us in comparing two equations when using slope intercept form, especially when the y-intercept stays the same

  3. Direct Variation Some equations exhibit direct variation • Direct variation means that the y variable has a direct relation to x i.e. no y-intercept • Follows the form • Where a is called the constant of variation

  4. Y X Graphing with Direct Variation To graph direct variation, we follow the same rules for slope intercept, except b=0 • y=2x • y-intercept=0 • Slope=2

  5. Y X Graph then find when x=2 y=2x y-75x=0

  6. Y X Graph then find when x=2 y=-4x y=.5x

  7. Y X Find a, then graph y=2, and x=4 y=26, and x=-2

  8. Y X Find a, then graph y=15, and x=-6 y=-4, and x=-18

  9. Practical Example • The number s of tablespoons of salt needed in a saltwater fish tank varies directly with the number w of gallons of water in the tank. A pet shop owner recommends adding 100 tablespoons to a 20 gallon tank. • Find the constant of variation for the example • How many tablespoons should be added for a 30 gallon tank?

  10. Practical Example • An object that weighs 100 pounds on Earth would weigh just 6 pounds on Pluto. Assume that weight P on Pluto varies directly with the weight E on Earth. • Find the constant of variation for the example • How much would you weigh on Pluto?

  11. Most Important Points • Two variables show direct variation when the y-intercept is 0 • The constant of variation is an index of that variation which is also the slope of the line

  12. Y X Practice y=-4x+5

  13. Y X Practice

  14. Y X Practice

  15. Y X Y-intercepts Formulas are useful because we’re able to see relationships that occur when we change components of the equations What happens when we begin to change the y-intercept? Graph y=2x+2 y=2x-3

  16. Parallel Lines How do we define parallel lines? Parallel: Two lines that will never touch i.e. two lines that have identical slopes with different y-intercepts

  17. Y X Practice

  18. Practical Example • Louise and Erika are trying to save money to buy matching winter coats. They both currently have $20 saved, but need to get a total of $95 to buy their coats by December first. They both make $40 per week. Louise saves $15 of her check for her coat. Erika only saves $11. Will they both make their goal?

  19. Y X Practice December 1st is 6 weeks away

  20. Y X Practice

  21. Homework 4.6 3-9 odd, 12-22 even, 23-25, 29-34

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