The slope of a line, m, is a rate of change which is constant in linear equations.
When a line passes through the points
(x_{1}, y_{1}) and (x_{2}, y_{2}), the slope, m, is expressed:
Slopes may be positive, negative, zero, or undefined(does not exist).

Lines that have positive slope, rise from the lower left to the upper right on the axes. They go "up hill". 

Lines that have negative slope, decline from the upper left to the lower right on the axes. They go "down hill". 

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

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

Depending upon the given information, equations of lines can take on several forms:
• Slope Intercept Form:
y = mx + b
Use this form when you know, or can find, the slope, m, and the yintercept, b.
• Point Slope Form:
y  y_{1} = m(x  x_{1})
Use this form when you know, or can find, a point on the line (x_{1}, y_{1}), and the slope, m.
• Standard Form:
Ax + By = C
The A and B values in this form cannot be zero. Use when asked to state the answer in Standard Form.
May also be Ax + By  C = 0.
• Horizontal Line Form:
y = 7 (or any Real 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. Every point on this line has a yvalue of 7. When writing the equation, we have
y = mx + b
y = 0x + 7
y = 7.
Note: The equation of the xaxis is y = 0.
• Vertical Line Form:
x = 5 (or any Real number)
Lines that are vertical have no slope (it does not exist, undefined). They have "rise", but no "run". The rise/run formula for slope always has a zero denominator and is undefined. Every point on this line has an xvalue of 5.
Note: The equation of the yaxis is x = 0.
Note:
•
Lines that are parallel have equal slopes.
•
Lines that are perpendicular have negative reciprocal slopes.
(A line with m = 4 will be perpendicular to a line with m = ¼)
