Today in class students worked out the parts of an equation that describes a proportional relationship. y = kx where y is the output result of multiplying the constant of proportionality, or unit rate, times any input x.
Answers to HW: 1.a. The car travels 65 miles in 1 hour; the car is traveling 65 miles per hour; 65 miles per hour is the constant of proportionality. b. The car travels 97.5 miles in 1.5 hours. c. It take the car 2/5 of an hour, or 0.4 hours, or 24 minutes to travel 26 miles. 2.a. w = 17b or b = 1/17 w b. 867 fluid ounces because 17 times 51 = 867 c. 3 bottles because 51/17 = 3 3. x = 1.61y and y = 1/1.61 x OR y = 0.62x 4.a. number of quarters number of toonies 1 1/8 16 2 20 2.5 24 3 b. 1/8 means that one eighth of a toonie equals one quarter 5. The scale factor down the first table is times 3/2, down the second table is times 2, and down the third table is times 3. The unit rate, or constant of proportionality, is 1:5 for the first table, 1:1/4 for the second table, and 1:3/5 for the third table x | y x | y x | y 2 | 10 12 | 3 5 | 3 3 | 15 20 | 5 10 | 6 7 | 35 40 | 10 30 | 18 1 | 5 1 | 1/4 1 | 3/5
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