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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 $\frac{1}{25}$

Martha and Peter are making cookies for their school bake sale. The table shows the number of cookies, y, that they can produce in x minutes.

Time in minutes, x
Number of cookies, y
13
286
26
572
39
858
52
1144

The relationship between the number of cookies they have baked and the time it has taken to bake them is linear.
Determine the constant of variation.

Solution: