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# Module 5 topic 1

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### Module 5 topic 1

1. 1. Module 5 Topic 1<br />Applications of Linear Functions<br />
2. 2. Example 1<br />Similar Problem: If y = 18 when x = 3, find y when x = 5.<br />Direct Variation is y = kx<br />y = kx<br />18 = k(3)<br />6 = k<br />y = 6x<br />y = 6(5)<br />y = 30 <br />
3. 3. Example 2<br />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).<br />w = 5.5h - 145<br />w = 5.5(76) - 145<br />w = 418 - 145<br />w = 273 inches <br />
4. 4. Example 3<br />Similar Problem: What is the direct variation equation for this graph?<br />Use the ordered pairs (0, 0) and (6, 4).<br />Find the slope first.<br />m= (y2 - y1) ÷ (x2 - x1)<br />m= (4 - 0) ÷ (6 - 0)<br />m= 4 ÷ 6 or 4/6 which reduces to 2/3<br />Since the line crosses through the origin the equation of the line is y = mx.<br />y= 2/3 x<br />
5. 5. Example 4<br />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?<br />books = \$15 membership fee + \$6.99 per book<br />b = \$15 + \$6.99x <br />
6. 6. Example 5<br />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?<br />gas left in the tank (y) = -0.04 gallons per mile (x) + 18 gallons<br />y = -0.04x + 18 <br />
7. 7. Example 6<br />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. <br />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. <br />
8. 8. Example 7<br />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?<br />If it uses 0.04 gallon per mile then it is decreasing as you use it.<br />y = -0.04x + 16 <br />
9. 9. Example 8<br />Similar Problem: Find the constant of variation in the following problem. When x = 1, y = 8.<br />When x = 1 the ordered pair is (1, 0).<br />When y = 8 the ordered pair is (0, 8). <br />Use these ordered pairs to find the slope or the constant of variation.<br />k= constant of variation and m = slope which are the same<br />k= m = (8 - 0) ÷ (0 - 1)<br />k= m = 8 ÷ -1 which is -8 <br />