 Slope
Slope refers to the slant of a line.
The formula for slope is
Some other renditions of the formula for slope are
A horizontal line has slope of 0.
A vertical line has undefined slope.
 SlopeIntercept Form of a Linear Equation
 The form: y = mx + b
 where
 m is the slope
 the point (0, b) is the yintercept
 Use when:
 given the slope and yintercept (plug them in).
 Any equation of a nonvertical line can be put in slopeintercept form.
 Vertical lines have the form x = a.
 PointSlope Form of a Linear Equation
 The form: y  y_{1} = m(x  x_{1})
 where
 m is the slope
 the point (x_{1}, y_{1}) is a specified point on the line.
 Use when:
 given two points
 calculate the slope, m, between the two points
 plug m and either point into the formula
 given the slope and a point (plug them in).
 Parallel and Perpendicular
Lines with the same slope are parallel.
 y = 2x  1
 y = 2x + 3
 m = m = 2
 The red and blue lines are parallel.
Lines with the product of their slopes equal to 1 are perpendicular.
 y = 0.5x + 1
 m·m = 1
 m·m = 1
 The red and blue lines are both perpendicular to the purple line.
 To determine if two lines are parallel, perpendicular, or neither:
 Determine the slope of each line.
 The lines are parallel if the slopes are equal.
 The lines are perpendicular if the product of the slopes is 1.
 Otherwise, the lines are neither parallel nor perpendicular.
 Graphing from SlopeIntercept Form

 Read the slope m and yintecept (0, b) from the equation.
 Plot the yintecept (0, b).
 Write the slope as a rational number, m = c/d.
 Starting at the yintercept, move c units vertically and then d units horizontally, and plot a point there.
 c > 0 means up and c < 0 means down.
 d > 0 means right and d < 0 means left.
 Draw a straight line through the two points.
 Graphing from PointSlope Form

 Read the slope m and point (x_{1}, y_{1}) from the equation.
 Plot the point (x_{1}, y_{1}).
 Write the slope as a rational number, m = c/d.
 Starting at the point (x_{1}, y_{1}), move c units vertically and then d units horizontally, and plot a point there.
 c > 0 means up and c < 0 means down.
 d > 0 means right and d < 0 means left.
 Draw a straight line through the two points.
