Linear Equations in Two Variables

1
Linear Equations in Two Variables
2
Slope of a Line

• If (x1, y1) and (x2, y2) lie on a line and x1?x2,
  the slope of the line containing them is
• (y2- y1)/(x2- x1).

3
More on Slope

• Notice that the slope of a vertical line is
  undefined.
• The slope of a horizontal line is 0.

4
Graph of a Line

• The graph of the equation ymx b is
• A line whose slope is m and whose y-intercept is
  b.

5
The Equation of a Line

• If a line contains the point (x1 , y1) and has
  slope m, its equation is
• y - y1 m(x x1)

6
Parallel and Perpendicular Lines

• Two non vertical lines are parallel if and only
  if their slopes are equal.
• Two non vertical lines are perpendicular if and
  only if the product of their slopes is 1.

7
Vertical Lines

• Any two vertical lines are parallel.
• Any vertical line is perpendicular to any
  horizontal line.