What are three ways to describe slope?

 

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Here are some ways to describe slope:

(1) Verbally slope indicates the steepness of a line (the sign indicates direction and the absolute value describes the steepness -- the larger the absolute value the steeper the graph.) This is related to the grade of a hill or the pitch of a roof.

(2) Algebraically slope is typically represented by m: for instance the equation of a line can be written as y=mx+b where m represents the slope. Also the slope formula where `m=(y_2-y_1)/(x_2-x_1) ` . However, some linear functions use other letters for the value that is the slope of the graph such as a direct variation y=kx where k is the constant of proportionality.

(3) Graphically slope is often represented as rise over run, or `(Delta y)/(Delta x) ` , or the ratio of the change in the vertical direction to the change of the horizontal.

(4) In modelling situations we say that the slope is the constant (or average) rate of change.

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