of a passing through the
is the of the vertical change
to the horizontal change
between the points. The
is most commonly used to represent the slope.
rise and run is sometimes used to describe the slope of a line, especially when the line is given graphically. Rise corresponds to and run corresponds to
With this information, the definition of the slope of a line can be written in terms of rise and run.
Because the of a is constant, any two points on the line can be used to find the slope – either algebraically with the or graphically as shown below.
The sign of each distance corresponds to the direction of the movement between the points. Moving to the right, the run is positive. Conversely, moving to the left, the run is negative. Similarly, moving up yields a positive rise while moving down gives a negative rise.