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9.1: Inverse and Joint Variation

9.1: Inverse and Joint Variation. Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models. Review of Direct Variation:. Linear function whose graph passes through the origin y= kx , where k is the constant of variation

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9.1: Inverse and Joint Variation

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  1. 9.1: Inverse and Joint Variation Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models

  2. Review of Direct Variation: • Linear function whose graph passes through the origin • y= kx, where k is the constant of variation • “y varies directly with x” (y = kx) • If every is the same for a set of data pairs, then it is direct variation EXAMPLE: • k = y/x = ½ for every data pair • y varies directly with x • y = (1/2) x

  3. Inverse Variation: • “y varies inversely with x” • k = x∙y • If every x∙y is the same for a set of data pairs, then it is inverse variation EXAMPLE: • k = xy= 30 for each data pair • Inverse variation model:

  4. Distance, Speed, and Time • Distance, speed, and time are all related. Look at the triangle below: Which quantities vary indirectly with each other? As one goes up, the other does too. Which quantities vary directly with each other? As one goes up, the other goes down d s t

  5. Tell whether x and y show direct variation, inverse variation, or neither. • Solve for y. Does it look like a direct or inverse variation model?? • xy = 4.8 • x = • y –x = 2 Inverse variation Direct variation neither

  6. Does the following show inverse variation, direct variation, or neither? Direct: y = -2x

  7. x and y vary inversely and y = 6 when x = 1.5:a.) write and equation that relates x and yb.) Find y when x = 4/3 a.) Find the constant, k: k = xy k = (1.5)(6) = 9 Write equation using k: b.) Find y when x = 4/3:

  8. YOU TRY: x and y vary inversely and x = 7 when y = 1. Write and equation relating x and y and find y when x = 3.

  9. The volume of gas in a container varies inversely with the amount of pressure. A gas has volume 75 in 3 at a pressure of 25 lb/in2. Write a model relating volume and pressure. “Volume varies inversely with pressure” “ y varies inversely with x “ k = V∙P = 75∙25 k= 1875 V =

  10. The grade you earn in math varies inversely with the number of minutes per night you watch television. If you watch 90 minutes per night, you get a 60 in math. • What is the constant of variation? • How much television can you watch if you want to make a 70? • You cut back on your television to only 75 minutes a night, what grade will you make in math? • What is the maximum amount of television you can watch and still make a 100?

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