Parallel and Perpendicular Lines

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Parallel and Perpendicular Lines
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From Intermediate Algebra
Equations of lines to Remember
Slope-Intercept Form

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

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 in this equation.

General Form

• Commonly used to write linear equation problems
  or express answers

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Parallel and Perpendicular
The slope is a number that tells "how steep" the
line is and in which direction. So as you can
see, parallel lines have the same slopes so if
you need the slope of a line parallel to a given
line, simply find the slope of the given line and
the slope you want for a parallel line will be
the same.
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
(flip it over) and make it negative.
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Let's look at a line and a point not on the line
Let's find the equation of a line parallel to y
- x that passes through the point (2, 4)
y - x
What is the slope of the first line, y - x ?
(2, 4)
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This is in slope intercept form so y mx b
which means the slope is 1.
So we know the slope is 1 and it passes through
(2, 4). Having the point and the slope, we can
use the point-slope formula to find the equation
of the line
-1
4
2
Distribute and then solve for y to leave in
slope-intercept form.
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What if we wanted perpendicular instead of
parallel?
Let's find the equation of a line perpendicular
to y - x that passes through the point (2, 4)
y - x
(2, 4)
The slope of the first line is still 1.
The slope of a line perpendicular is the negative
reciporical so take 1 and "flip" it over and
make it negative.
1
2
4
Distribute and then solve for y to leave in
slope-intercept form.
So the slope of a perpendicular line is 1 and it
passes through (2, 4).