If the function y = xa − 31 is a linear function, what is the value of a?

The question is pretty poorly worded, but I think you just haven't been too successful at putting it into the Internet. The fact the a is after x probably indicates you mean x^a. In any case that is the only way there would be enough information to find the value of a.

Now, a linear function takes the form y = mx + c. Therefore, where m is 1 in this case, there must be a direct comparison with y = x ^a - 31. So how can the x be raised to an exponent then, I hear you ask. Well it is raised to the power 1. We just omit the 1 because it is somewhat superfluous.

In conclusion a = 1. I hope this helps you