That depends on which math course you're taking. In calculus, slope is the instantaneous rate of change (see "limits" in your textbook).
In statistics it's the average change over the period under review, for the parameters in question (for example, the annual rate of inflation for foodstuffs 1960-2010).
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You're getting confused on semantics. Slope, tangent line and instantaneous rate of change are all different ways of saying the same thing. The tangent line is a straight-line extension of a curve at a single point on that curve. The concept is similar to tying a string onto a rock and swinging the rock in a circle. When you release the string, the rock will travel in a straight line (the tangent line), with the direction of travel determined by the instantaneous rate of change of the direction of the rock at the instant before it was released.
In other words, slope = tangent line = instantaneous rate of change at the point where the tangent line touches the curve.
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