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on the highway trip a midsize car traveled 208 miles on 4 gallons of gasoline. which direct variation equation describes the relationship between gallons of gasoline x and distance traveled in miles y

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It is a direct variation.

y = k x

You can solve for k .

y  = 208

x = 4

k= ??

y = k * x

208 = k * 4   Divide by 4

208 / 4 = k

k = 52

So the equation becomes

y = 52 x