The Slope of a Line
Let P = (x1,y1) and
Q =(x2,y2) be two points
on the Cartesian plane. The slope
of the straight line passing through P and Q is
This is sometimes written as
we say "the slope is equal to the change in y relative to
the change in x" .
Note that m
= tan θ, where θ is the angle of inclination.
Note also that if m
> 0, the line is rising (or increasing). If m < 0, the
line in falling (or decreasing) and if m = 0 the line is horizontal.
The slope of the line determined by two points is used in many practical
situations, such as finding the average velocity (or change in distance
over time) and finding the average marginal cost (or change in cost per
A vertical line has undefined slope because all points on the
line have the same x-coordinate . As a result the formula used
for slope has a denominator of 0, which makes the slope undefined.
Index | The Slope of a Tangent