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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 $\frac{1}{25}$

Students in a science class recorded lengths of a stretched spring, as shown in the table below..

Distance Stretched
(cm)
Mass
(grams)
5
50
10
100
15
150
20
200
25
250

The relationship between the distance stretched x and the mass of an object on the spring is linear.
Determine the constant of variation.

Solution: