Explain how to use a table to write an equation that represents the relationship in the table.

It depends.

In the most general case, you use an interpolating function such as a Lagrange polynomial to ensure that the equation matches the given points.

More commonly, you will check to see if the points given in the table are evenly spaced. If they are, then you can examine differences between function values to see what pattern there might be.

If first-differences are constant, the relationship is linear.
If second diferences are constant, the relationship is quadratic. This pattern continues so that n-th level differences being constant means the relationship can be modeled with an n-th degree polynomial.

If differences at each level match those at the level before, the relationship is exponential.

If the table values or the differences are periodic, then it may be possible to model the relationship as a sum of sine and cosine functions.

If table values are not evenly-spaced, they can be plotted on a graph to see if there appears to be a relationship that is obvious.

Table values can be entered into a spreadsheet or calculator to see if they can be matched by any of the available regression functions.