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slope

Slope is a measure of the steepness or incline of a line or surface. In two-dimensional analytic geometry, the slope of a line is the ratio of the vertical rise to the horizontal run between two points on the line. If a line passes through points (x1, y1) and (x2, y2), its slope is m = (y2 − y1) / (x2 − x1). A positive slope means the line rises as it moves to the right; a negative slope means it falls. A zero slope indicates a horizontal line, while an undefined slope indicates a vertical line. The slope is also the derivative dy/dx for a function y = f(x), so it represents the instantaneous rate of change.

In algebra, the slope is the parameter m in the linear equation y = mx + b, where b

Slope has broad applications, including determining road and rail grades, roof pitch, and drainage or erosion

Common properties include that slope depends on units; horizontal lines have slope zero, vertical lines have

is
the
y-intercept.
In
higher
dimensions,
slope
generalizes
to
the
gradient
of
a
function,
which
points
in
the
direction
of
steepest
ascent
with
magnitude
equal
to
the
rate
of
increase.
risk;
in
geology
and
geomorphology,
for
assessing
slope
stability;
in
GIS,
slope
maps
characterize
terrain;
and
in
statistics,
the
slope
of
a
regression
line
indicates
the
strength
and
direction
of
a
relationship.
undefined
slope.