Problem: The price of 5 drinks is $10. Form an equation that relates the cost (y) with the number of drinks (x).
Answer: y = 2x
Reason: The unit price is k = y/x = 10/5 = 2 dollars per drink. So y = kx becomes y = 2x. Note that plugging in x = 5 leads to y = 10.
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Problem: A car can travel 200 miles on 8 gallons of gas. How far can it travel using five gallons?
Answer: 125 miles
Reason: We have y = 200 and x = 8 lead to the constant of proportionality of k = y/x = 200/8 = 25. The direct proportion equation y = kx becomes y = 25x. Then we plug in x = 5 to lead to y = 125.