The slope of a line
is a rate of change and is represented by m.
When a line
passes through the points
(x_{1}, y_{1}) and (x_{2},
y_{2}), the slope is
m =
.

Lines that have a positive slope, rise from
lower left to upper right. They go up hill. 

Lines that have a negative slope, decline
from upper left to lower right. They go down hill. 

Lines that are horizontal have a slope of zero.
(There is no "rise", creating a zero numerator.) 

Lines that are vertical have no slope (undefined
slope). (There is no "run", creating a zero
denominator.) 

Lines that are parallel have equal slopes. 

Lines that are perpendicular have negative
reciprocal slopes.
(such as m = 2 with m = 1/2) 

Equations of line can take on several forms:
Slope Intercept Form:
[used
when
you know, or can find, the slope, m, and the yintercept,
b.]
y = mx
+ b
Point Slope Form:
[used when
you know, or can find,
a point on
the line (x_{1}, y_{1}), and the slope,
m.]
Horizontal Line Form:
y = 3 (or
any number)
Lines that are horizontal
have a slope of zero. They have "run", but no
"rise". The rise/run formula for slope
always yields zero since rise = 0.
y = mx + b
y = 0x + 3
y = 3
Vertical
Line Form:
x = 2 (or
any number)
Lines that are vertical have no slope
(it does not exist). They have "rise", but no
"run". The rise/run formula for slope always has a
zero denominator and is undefined.
