08242012, 11:54 AM


In the case of that particular table, I think it would help a lot to try to figure out what would happen for the inbetween values (in this case, the even numbers). You've already noticed that if x increases by 2, y increases by 110, so it makes sense that if x increases by 1, y will increase by 55. (NB: That only works for linear relationships! Your son will get to a point, probably this year, where you can't do that anymore. But for now, use it.)
That numberthe amount y increases if x increases by 1is the coefficient on the x term in the equation. (It's also the slope of the line, when you graph it.) y = 55x +/ ????
To figure out what number to add to that, test it out with the first number. You can plug in the x and y values you've got on the chart. For instance, in your first row, x is 1 and y is 55. If you put that into the equation, you get 55 = 55*1 +/ ????. Well, since 55*1=55, in this case we don't need to add anything. And you're done: The equation is y = 55x.
It's never a bad idea to run a couple more lines of the data table through the equation, to make sure it really works at all points.
I hope that made some sense. I don't know any tricks for this; you just get good at seeing the pattern after awhile. I'm curious to see others' tricks, though!
