posted by johnny .
What similarities and differences do you see between functions and linear equations, Are all linear equations functions? Is there an instance when a linear equation is not a function? Create an equation of a nonlinear function and provide two inputs to evaluate.
A straight line, unless vertical, has one and only one value of the dependent variable (y for example) for every value of the independent variable (x for example). It is therefore a function unless it is vertical. Therefore I claim that all linear equations are functions except one of form x = constant.
An easy non-linear function is y = x^2
Here there is one and only one value of y for every value of x so it is a function. You can put in a couple of values of x and find y, for example (0,0) and (3,9).
Notice that x is NOT a function of y in this equation because there are TWO values of x for every y.