What is the difference between a linear equation and a quadratic equation? (in 7 sentences)

A linear equation in two variables doesn't involve any power higher than one for either variable. It has the general form Ax + By + C = 0, where A, B and C are constants. It's possible to simplify this to y = mx + b, where m = (-A / B) and b is the value of y when x = 0. A quadratic equation, on the other hand, involves one of the variables raised to the second power. It has the general form y = ax2 + bx + c. Apart from the adding complexity of solving a quadratic equation compared to a linear one, the two equations produce different types of graphs.