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There are many examples of linear relationships that you could use.
On the one hand, you could create a situation that is perfectly linear, such as determining the total income of the local paper boy as a function of the number of papers that he delivers. The income function will have the form y = mx + b, where y is the paper boy's income, m is the income per paper, x is the number of papers, and b is any fixed income (which could also be zero).
I suspect, however, that the instructions that were given to you suggest that you find a data set that is linear-ish, rather than coming up with a perfectly linear equation. Finding suitable real data can be difficult (and exhausting). A popular approach is to select an Olympic sport (because records are easy to obtain, see www.olympic.org), and record the times in that event over several years. Surprisingly, over the long-term, the improvements in times tends to be close to linear.
If it is permissible to create a fictitious data set, you could also "record" the height and weight of classmates. Provided that you avoid those who deviate extremely from "normal", the relationship should be fairly linear. You could also make up something about the number of fruit trees that various farmers have and the total yield of their crop, or the number of books in a student's backpack and the total weight of the pack. Pretty much anything that is more or less proportional will work.