how do I write an equation based on a two-column table of data?
You need to find a relationship between the independent (we'll call x) and dependent (we'll call y) variables first.
Sometimes it's simple proportionality: y=px where p is a common constant of proportionality for each row of the table; sometimes it's linear: y=px+a where as well as p we have a sort of displacement called the y intercept which is added after applying p, you can tell if's linear by lookin at the difference of consecutive x and y values in the table. If we take two y values y1 and y2 and their corresponding x values x1 and x2 and work out p=(y1-y2)/(x1-x2) for all corresponding listed values in the table, and this calculated value of p is the same for all of them then we have a linear relationship y=px+a. We find a by taking any single row (x, y value) and then a=y-px for whatever (x,y) we picked. The value of a may be positive or negative.
If it's inverse proportionality the rule xy=p applies to every corresponding x and y value and we can also have the relationship y=(p/x)+a so a=y-(p/x) for all corresponding pairs (x,y).
There are other more complicated relations that can be made into an equation, but the most likely ones for this type of question are the linear relationships, direct and inverse prortionality. Read More: ...