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Module 5 Topic 1 Applications of Linear Functions
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Example 1 Similar Problem: If y = 18 when x = 3, find y when x = 5. Direct Variation is y = kx y = kx 18 = k(3) 6 = k y = 6x y = 6(5) y = 30
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Example 2 Similar Problem: An equation which represents the average weight in pounds of an adult male of a given height in inches is w = 5.5h - 145. Predict the weight in pounds of an average male with a height of 6'4" (76 inches). w = 5.5h - 145 w = 5.5(76) - 145 w = 418 - 145 w = 273 inches
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Example 3 Similar Problem: What is the direct variation equation for this graph? Use the ordered pairs (0, 0) and (6, 4). Find the slope first. m= (y2 - y1) ÷ (x2 - x1) m= (4 - 0) ÷ (6 - 0) m= 4 ÷ 6 or 4/6 which reduces to 2/3 Since the line crosses through the origin the equation of the line is y = mx. y= 2/3 x
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Example 4 Similar Problem: Angel joined a paperback book club for a $15 membership fee, plus $6.99 per book. Write an equation that best represents the money Angel spent? books = $15 membership fee + $6.99 per book b = $15 + $6.99x
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Example 5 Similar Problem: You drive a car that holds 18 gallons of gasoline. Your car uses 0.04 gal per mi. Write an equation that best represents the amount of gas left in the tank? gas left in the tank (y) = -0.04 gallons per mile (x) + 18 gallons y = -0.04x + 18
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Example 6 Similar Problem: Farley bought $6 worth of school supplies plus pencils at $0.50 per pencil. What is the rate of change in this sentence. The rate of change is the item that you control how much you purchase so Farley can control how many pencils he purchases so the rate of change is $0.50 per pencil.
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Example 7 Similar Problem: You drive a car that holds 16 gallons of gasoline. Your car used 0.04 gal per mi. Write an equation that best represents the amount of gas left in the tank? If it uses 0.04 gallon per mile then it is decreasing as you use it. y = -0.04x + 16
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Example 8 Similar Problem: Find the constant of variation in the following problem. When x = 1, y = 8. When x = 1 the ordered pair is (1, 0). When y = 8 the ordered pair is (0, 8). Use these ordered pairs to find the slope or the constant of variation. k= constant of variation and m = slope which are the same k= m = (8 - 0) ÷ (0 - 1) k= m = 8 ÷ -1 which is -8
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