Finding the (in)dependent value on a Coordinate Plane?

Question

If I' am given a dependent value and am asked to find it's corresponding independent value, how could I go about doing this (assuming I am given other ordered pairs as well)?

Answer 1

It depends on how much you know about the ordered pairs. If we are dealing with a function, but you are told nothing further about it, then no number of ordered pairs is enough to be able to determine the independent value associated with a given dependent value with certainty. For example, if you are given three ordered pairs and they all lie on a line, you still don't really know for sure that the function is linear, since it could be piecewise or it could be the points at which a line intersects a much more complicated function.

In general, though, you want to use the points you are given in order to find the equation for the function. If you are told it is a linear equation, two points is sufficient. Given the points (x1, y1) and (x2, y2), the equation of the line in point-slope form would be y - y1 = m(x - x1), where m = (y1 - y2) / (x1 - x2). Various other types of functions may require you to know more than two points and the algebra to determine the equation may be more complicated.