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Direct Variation

Direct Variation. Section 2.6 Goal: Write and graph direct variation equations. Warm-up.

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Direct Variation

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  1. Direct Variation Section 2.6 Goal: Write and graph direct variation equations.

  2. Warm-up 1. A company sells jeans and T-shirts. J represents jeans and T represents T-shirts in the equations below: 2J + T = $50J + 2T = $40 Sarah buys one pair of jeans and one T-shirt. How much does she pay for her entire purchase? F. $10 G. $20 H. $30 J. $70 K. $90 2. A flight with a low-cost airline travels 9  103 miles per hour for 3  10-2 hours. How far has this cheap flight traveled? F. 135 miles G. 270 miles H. 900 miles J. 1350 miles K. 2700 miles 3. Marta has just bought a new pair of tennis shoes. She wants to wear the new running shoes to run up and down a hill near her house. The measurements of the hill can be placed on a two dimensional linear graph on which x = 5 and y = 165. If the line crosses the y axis at 15, what is the slope of this hill? A. 10 B. 20 C. 30 D. 36 E. 75

  3. Direct Variation: 2 variables x and y show direct variation, or vary directly if y = kx, where k is a nonzero constant called the constant of variation.The graph of y = kx is a line through the origin with slope k.

  4. Graph y = ¾x

  5. The variables x and y vary directly. x=3 when y=-9.Write an equation that relates x and y. This is the equation that relates x and y. k is called the constant of variation.

  6. The variables x and y vary directly. x=22 when y=-2.Write an equation that relates x and y. This is the equation that relates x and y. k is called the constant of variation.

  7. A recipe for fruit punch uses 2 lemons to make 7 cups of punch. Write an equation relating the number of servings y to the number of lemons x. How many cups of punch can you make if you have 8 lemons? This is the equation that relates x and y.

  8. An athlete ran 440 yards. Her coach recorded the number of seconds x and the number of yards y during that run. Tell whether the data shows direct variation. If so, write an equation relating x and y. x and y vary directly. This is the equation that relates x and y.

  9. Assignment Textbook pages 103-105 Problems 18-25, 27-35, 38-39, 61-66

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