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Warm-Up

6 minutes. Warm-Up. Solve each equation. 1) 27 = c(-4). 2). 3). 4). 5) 2(4y + 1) = 3y. 1.4.1 Direct Variation and Proportion. Objectives: Write and apply direct variation equations. Direct Variation. the distance “varies directly” as the time. d = 10t.

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Warm-Up

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  1. 6 minutes Warm-Up Solve each equation. 1) 27 = c(-4) 2) 3) 4) 5) 2(4y + 1) = 3y

  2. 1.4.1 Direct Variation and Proportion Objectives: Write and apply direct variation equations

  3. Direct Variation the distance “varies directly” as the time d = 10t An equation of the form y = kx, where k is a constant, expresses direct variation. k is called the constant of variation.

  4. Example 1 Find an equation of variation where y varies directly as x, and y = 4 when x = 6. y = kx 4 = k(6)

  5. Practice Find an equation of variation where y varies directly as x. 2) y = 50 when x = 80 1) y = 84 when x = 12

  6. Example 2 When traveling at a constant rate, Heidi drives her car 12 miles in about 15 minutes. At this rate, how long would it take Heidi to drive 30 miles? d = rt 37.5 minutes

  7. Example 3 The cost of the electricity used by a light bulb varies directly as the time the bulb is on. Four hours of use cost twelve cents. How much will 11 hours of use cost? Let c = the cost of the electricity in cents Let t = the time the bulb is used in hours c = kt c = 3(11) 12 = k(4) 3 = k c = 33 c = 3t 33 cents

  8. Practice 1) The cost (c) of operating a TV varies directly as the number (n) of hours it is in operation. It costs $14 to operate a standard-size color TV continuously for 30 days. At this rate, about how much would it cost to operate the TV for 1 day? 1 hour? 2) The weight (v) of an object on Venus varies directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 150 lb on Earth weigh on Venus?

  9. Homework p.33 #15,19,21,23,27,29,33,35

  10. Brain Teaser A snail creeps 4 feet up a wall during the daytime. After all the labor it does throughout the day, it stops to rest a while... but falls asleep!! The next morning it wakes up and discovers that it has slipped down 2 feet while sleeping. If this happens every day, how many days will the snail take to reach the top of a wall 16 feet in height?

  11. 5 minutes Warm-Up In the following exercises, y varies directly as x. Find the constant of variation, and write an equation of variation that relates the two variables. 1) y = 21 when x = 7 2) y = -2 when x = 9 3) y = 0.6 when x = -3

  12. 1.4.2 Direct Variation and Proportion Objectives: Write and solve proportions

  13. If , then ad = bc. a c = b d Cross-Product Property of Proportions For b  0 and d  0:

  14. 35 87.5 = 4 x 35 87.5 35 x 350 4 x Example 1 Solve. 35x = 350 x = 10

  15. Example 2 Solve. Check:

  16. Example 3 The ratio of weight on Jupiter, WJ, to weight on Earth, WE, is given by . The rover Sojourner weighed 24.3 pounds on Earth. Suppose that Sojourner was sent to Jupiter instead of Mars. a) Find Sojourner’s weight on Jupiter to the nearest tenth of a pound. 61.7 lbs.

  17. Example 3 The ratio of weight on Jupiter, WJ, to weight on Earth, WE, is given by . b) Write a direct-variation equation that gives the weight of an object on Jupiter, WJ, in terms of its weight on Earth, WE.

  18. Homework p.33 #17,25,37,45,47,53,57

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