When used to describe an equation, "linear" means the function acts like an equation of the form f(x) = mx+b. This type of equation has a constant slope, so if you increase the value of the independent variable (x) by some amount the effect on the dependent variable f(x) is the same regardless of what the starting value of x is. For example, consider:
f(x) = 3x + 7.
If we start with x = 0, then f(0) = 7. Now if you add 1 to x (making it 1) the value for f(1) is 10, for an increase of 3 over what it was originally. Now if the original x was 10, then f(10)= 37, and if you add 1 to x, you can see that f(11) = 40, and so the corresponding increase in f(x)is still 3. Hence the equation is "linear."
A non-linear equation does not have a constant slope. Consider for example the equation f(x) = x^2. At x = 0 you have f(0) = 0, and for x = 1 you have f(1) = 1, for a difference of 1. But f(10) = 100, and f(11) = 121, for a difference of 21. Hence the equation f(x) = x^2 is not linear.
More details can be found here:
Linear equation - Wikipedia, the free encyclopedia
Linear Mode
