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

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Direct Variation and Proportion

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

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

Direct Variation the distance “varies directly” as the time t (hours)1234 d (km) d = 10t An equation of the form y = kx, where k is a constant, expresses direct variation. k is called the constant of variation.

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

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

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

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? c = kt Let c = the cost of the electricity in cents Let t = the time the bulb is used in hours 12 = k(4) 3 = k c = 3t c = 3(11) c = cents

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?

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

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? Brain Teaser

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 5 minutes 2) y = -2 when x = 9 3) y = 0.6 when x = -3

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

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

Example 1 35x = 350 x x x = x = Solve.

Example 2 Solve. Check:

Example 3 The ratio of weight on Jupiter, W J, to weight on Earth, W E, 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 lbs.

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

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