The difference quotient can be used to find the slope of a curve, as well as the slope of a straight line. After we find the difference quotient of a function and take the limit as two points get closer and closer to each other, we have a new function, called the derivative. To find the slope of the curve or line, we input the value of "x" to get the slope. The process of finding the derivative via the difference quotient is called differentiation.