Slope
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Slope is an idea in math.
[edit] Straight Line
"Rise over run" is the slope of a straight line. "Rise" is called the change in the y position ( how far up between two points), "Over" means to divide the "rise" by the "run". "Run" is called the change in the x position ( how far to the right between the points). The idea of x and y are part of the Cartesian coordinate system. y = mx + b is called the standard equation of a line. "m" ( the number in front of x ) is the slope in the standard equation of a line.
[edit] Curve
For curves the derivative gives the slope at a point. A derivative is an idea found in calculus. A derivative is written as df/dx or f'(x). df/dx is read as "the derivative of f with respect to x." f'(x) is read as " f prime". f'(x) is understood to mean the first derivative. Prime is French for first. The letter f is short for function. The letter d in df/dx is short for differential ( the change or difference ). f(x) is read "as f of x". f(x) is the y for the x. So df/dx means change of y over change of x. In a curve a slope is not the same for all points. The changes of y and x at a point on a curve are so small they seem not to exist. The slope is a limit of changes of y over changes of x.