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Warm Up

Warm Up. Sketch the graph and identify the slope and y intercept: 1. X = 2 Y = 4 2x + 4y = 8 2Y + 2 = 4 + 6x. Direct and Indirect Variation. I can solve for an unknown using direct and indirect variations. Direct/Indirect Variation.

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Warm Up

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  1. Warm Up • Sketch the graph and identify the slope and y intercept: 1. X = 2 • Y = 4 • 2x + 4y = 8 • 2Y + 2 = 4 + 6x

  2. Direct and Indirect Variation I can solve for an unknown using direct and indirect variations.

  3. Direct/Indirect Variation • Variationwill concern two variables; for example height and weight of a person, and how, when one of these changes, the other might be expected to change.

  4. Direct Variation • Direct variation exists if the two variables change in the same direction; i.e. if one increases, so does the other. • Example, the amount of time studying for a test is a direct variation of your test grade

  5. Indirect Variation • Indirect variationexists if one going up causes the other to go down. • Example: speed and time to do a particular journey; the higher the speed, the shorter the time.

  6. Direct or Inverse?? • Work with a partner. Discuss each description. Tell whether the two variables are examples of direct variation or inverse variation. • a. You bring 200 cookies to a party. Let n represent the number of people at the party and c represent the number of cookies each person receives. • b. You work at a restaurant for 20 hours. Let r represent your hourly pay rate and p represent the total amount you earn. • c. You are going on a 240-mile trip. Let t represent the number of hours driving and s represent the speed of the car.

  7. Direct Variation • When x and y are directly proportional, dividing these variables will give a constant result called the constant of proportionality or k. • We could also write this y = kx. Given the value of x, multiply this number by k to find the value of y.

  8. Example of direct variation • Given that y and x are directly proportional, and y = 2 when x = 5, find the value of when x= 15. We first find value of k, using y = kx 2 = k(5) K = 2/5 Now use this constant value in the equation y=kx for situation when x = 15. Y = (2/5) (15) Y = 6

  9. Direct Variation Practice y varies directly with x. If y = -4 when x = 2, find y when x = -6. Y = 12 • y varies directly with x. If y = 15 when x = -18, • find y when x = 1.6. Y = -4/3 • y varies directly with x. If y = 75 when x =25, find x when y = 25. Y = 25/3

  10. Example of Indirect Variation • Example: If it takes 4 hours at an average speed of 90 km/hour to do a certain journey, how long would it take at 120 km/hour? Y = K/x

  11. Indirect Variation Practice y varies inversely with x. If y = 40 when x = 16, find x when y = -5. X = -128 • y varies inversely with x. If y = 7 when x = -4, find y when x = 5. Y = -28/5

  12. Classify the following graphs as a) Direct b) Inverse c) Neither

  13. Tell whether x and y show direct variation, inverse variation, orneither. Explain your reasoning. • 1. y − 1 = 2x • 2. (1/5)y = x • 3. 2y = 1/x

  14. Real World Examples • The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are applied, the current is 4 amperes. What is the current when 18 volts are applied? • The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cm3 under pressure of 32 kg/cm2. What will be its volume under pressure of 40 kg/cm2?

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