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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 table shows the number of gallons of paints Mrs. Robinson used to paint the number of rooms.

Number of gallons of paint
Number of rooms painted
5
20
6
24
7
28
8
32

The relationship between the gallons of paint and the number of rooms painted is linear.
Determine the constant of variation.

Solution: