The slope of a linear relationship gives the constant rate of change of one of the variables in terms of the other. A nonlinear relationship has a different slope at every point because the rate of change of one variable in terms of the other is different at every point. The slope of a nonlinear relationship can be computed at any point and gives the rate of change at exactly that point.

We show a green line **tangent** to the curve at point **A**. The **slope of the tangent line is the slope of the curve** at that point. At point **A** the curve has a **slope of 1/4**, which means that **cost ($)** increases by only 1/4 if **Q** increases by one. At point **B** the slope of the curve, shown by the **orange tangent** line, is **1/2**, meaning that at that point cost rises by 1/2 for a one unit increase in **Q**. At **C** the curve has become much steeper, with a **slope of 3**. At point **C** cost increases by $3 for an increase in **Q** of one unit. The slope of the curve becomes steeper as we move to the right because cost is **increasing at an increasing rate**.