Download College Algebra 1-11 Parallel and Perpendicular Lines

GOAL: Master Parallel and Perpendicular Lines
Determining if lines are parallel or perpendicular from a graph is guess-work at best. We will investigate
better methods.
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Two lines are parallel if they have equal slopes

Two lines are perpendicular if their slopes are opposite reciprocals (

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Vertical lines are parallel to other Vertical lines (since their slopes are both undefined)
Vertical lines are perpendicular to Horizontal lines
)
EX: Determine if the following pairs of lines are parallel, perpendicular, or neither.
1) The line
and the line
.
They are opposite reciprocals so the lines are perpendicular.
2) The line
and the line
.
Even though they are in different forms (S.I.F. and P.S.F.) I still recognize their slopes.
The slopes are equal so the lines are parallel.
3) The line passing through
and the line passing through
The slopes are equal so the lines are parallel.
4) The line
and the line
They are opposite reciprocals so the lines are perpendicular.
5) The lines passing through
and
and the line passing through
The first line is horizontal, and the second line is vertical. So they are perpendicular.
.
6) The line
and the line
The lines do not have equal slopes, nor are they opposite reciprocals. They are neither parallel
nor perpendicular.
7) The line
and the line
.
Both lines are vertical (They are of the form
8) The line passing through
and
. They are parallel.
and the line passing through
The lines do not have equal slopes, nor are they opposite reciprocals. They are neither parallel
nor perpendicular.
9) The line
and the line
Finding the slope of the first line (by putting it into S.I.F):
Finding the slope of the second line
The slopes are opposite reciprocals so the lines are perpendicular
Writing Equations of Lines:
When required to create an equation parallel or perpendicular to a given line we are essentially given a
required slope!
EX: Find the equation of the line parallel to
We must be parallel to
We need
and passes through
ALL this tells us is that OUR slope must be
and passing through
Since the form wasn’t specified, I’m leaving it in P.S.F.
EX: Find the equation of the line perpendicular to
and passing through the point
We need to have a slope which is a opposite reciprocal of the slope of
its slope.
Let’s determine
Our slope must be
Also notice that
is on the y-axis, so it is our y-intercept. We should then use S.I.F.
EX: Find the equation of the line parallel to
and passing through
The line given is horizontal (Of the form
so a line parallel will also be horizontal.
All horizontal lines share the same y-coordinate, so our line is
Note that we could have also just said the slope was Zero.
(
EX: Find the equation of the line parallel to
)
and passing through
First find the slope of the given line:
Since we must make a line parallel to this it means our slope must also be
Please note any similarities in the y-intercepts of the two lines is merely coincidental.