How can you identify a linear relationships in tables, graphs, and written form?

A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In other words there is a one to one correspondence between values of f(x) and values of x.

If the values of f(x) and x for a linear function are written in the form of a table we find that each value of f(x) has a corresponding value of x that is unique. If a graph is drawn of the function it is always a straight line.

A linear function results in a graph that is a straight line, and the values of f(x) and x written as a table show a one to one correspondence.