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1. Change in y over change in x. For a linear equation, this is just m = (y2-y1)/(x2-x1) where (x1,y1), (x2,y2) are any two points on the line.

2. Evaluating the tangent of the angle relative to horizontal. For example, if a ramp has a 10 degree angle above horizontal, then the slope is tan(10).

3. For any differentiable function y in terms of x, dy/dx gives the expression for the slope of a tangent line through a point on y. If y = x3+1, then dy/dx = 3x2, and at the point (1,2), dy/dx = 3, so the slope at this point is 3. Finding the derivative of a function is very similar to finding the slope of two points on a function that are infinitely close together.

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Q: What are three ways of finding the slope?
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You have two ways you could label the axes. Depending on how you choose to do it,the slope of the graph could be pounds per year, or it could be years per pound.


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point-slope formula and finding the slope of the line.


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