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Find the constant of variation from a table

Determine the constant of variation.

Miles, x
Gallons, y
25
1
50
2
75
3
100
4

Compare the ratios to check for a common ratio.

Since the ratios are the same, the function is a direct variation. The constant of variation is $\frac{1}{25}$

The distance a wheel moved forward varies directly with the number of rotations. Look at the following table.

Number of rotations
Distance (ft)
10
90
12
108
14
126
16
144

Determine the constant of variation.

Solution: