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A new compact car can travel 288 miles on nine gallons of gas. The distance driven in miles y varies directly with the number of gallons of gas x. This situation can be represented by the equation y = 32x.

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Answer:

Explanation of why [tex]y = 32x[/tex] is correct.

Step-by-step explanation:

The number of miles that the car can drive can be written as a function of the number of miles that each gallon is capable of by this following function:

[tex]y = ax[/tex]

In which a is the number of miles each gallon runs.

A new compact car can travel 288 miles on nine gallons of gas. How many miles can it travel on one gallon? This can be solved by a rule of three.

288 miles - 9 gallons

a miles - 1 gallon

[tex]9a = 288[/tex]

[tex]a = 32[/tex]

So

y = 32x is a correct representation for this problem, since with each gallon of gas the car can run 32 miles.

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