Parallel _ Perpendicular Lines

							Parallel & Perpendicular Lines
           Algebra 1
               &
        Algebra 1 Honors
     Slope of Parallel Lines
• Two non-vertical lines
  with the same slope
  are parallel.
  Parallel Lines
y  3x  4
y  3x  2
The equations of two parallel
lines have the same slope, but
two different y-intercepts.
        Parallel lines have
         the same slope
If Line A has a slope of 4 (m = 4),
then which of these four lines is parallel
to Line A?
          Line B, m = 16
          Line C, m = 12
          Line D, m = 4
           Line E, m = 2/3
      y = 3x + 4 and
         y = 3x - 2
y = 3x + 4

                y = 3x -2
                            BACK
        Are the two lines:
 L1, through (-2, 1) and (4, 5)
 L2, through (3, 0) and (0, -2),
            parallel?
      (5)  (1)   4   2
m1                
     (4)  (2) 6     3
     (0)  (2) 2
m2             
      (3)  (0)   3
Properties of Perpendicular                Lines
            Perpendicular Lines
What angles are formed by perpendicular lines?


                                           Right angles
                                           which equal
                                           900.
  Slopes of Perpendicular Lines
• If neither line is vertical, then the slopes of
  perpendicular lines are negative reciprocals.
• If the product of the slopes of two lines is -1
  then the lines are perpendicular.
• Horizontal lines are perpendicular to vertical
  lines.

       9     11    99
                   1
       11    9     99
                         3
Perpendicular Slopesm1                 4
                         4         m2 
                          y-axis        3



    x-axis


 What can we say
 about the intersection
 of the two lines?
Write parallel, perpendicular, or neither for the
pair of lines that passes through (5, -9) and (3, 7)
and the line through (0, 2) and (8, 3).

       (7)  (9)    16
  m1                    8
        (3)  (5) You Try
                     2
       (3)  (2) 1   8   1    8
  m2                              1
       (8)  (0) 8  1   8  8
Rules and Properties
 All vertical lines are parallel
 and have undefined slope.
Rules and Properties
All horizontal lines are parallel
     and have a slope of 0.
   1
m
   3
                Remember parallel lines have the
                same slopes so if you need the
            1   slope of a line parallel to a given
         m     line, use the same slope.
            3

        3
   m    3
        1       Perpendicular lines have negative
                reciprocal slopes so if you need the
                slope of a line perpendicular to a
                given line, simply find the slope of
                the given line, take its reciprocal,
                and switch the sign to the opposite.
     1
  m
     3
     y  mx  b           Slope-Intercept Form

 •Useful for graphing since m is the slope and b is the y-intercept

 y  y1  mx  x1            Point-Slope Form

 •Use this form when you know a point on the line and the slope
 •Also can use this version if you have two points on the line
 because you can first find the slope using the slope formula and
 then use one of the points and the slope to build an equation.

  ax  by  c              Standard Form

•Commonly used to write linear equation problems or express answers
Step1 – Steal Underwear
Step 2 –
Step 3 - Profit
Parallel & Perpendicular Lines
         Algebra 1 &
       Algebra 1 Honors