# Parallel Lines

``` Parallel
Lines = Lines in the same plane that
never intersect.
 Review:

Slope-Intercept form:
y = mx+b
 Write
an equation in slope-intercept form for
both of the lines below….what do you notice?
y = ⅔x + 5
y = ⅔x - 3
Parallel
Lines have the SAME slope
and DIFFERENT y-intercepts.

To determine whether lines are parallel, you just
compare the slopes and the y-intercepts…

If slopes are the same and different y-intercepts


If slopes are the same and the same y-intercepts


– the lines are parallel
- you have the same line
If slopes are different

– the lines are not parallel
1.
y = -⅓x + 5
and
2x + 6y = 12
2.
-6x + 8y = -24
and
y = &frac34;x - 7
3x + 4y = 12
and
y = &frac12;x + 5
1.
Identify the slope of the given line
2.
Write an equation in Point-Slope form using
the identified slope and the given point.
y – y1 = m(x – x1)
3.
Convert to Slope-Intercept form (solve for y)
y = mx + b
 Write
an equation in slope-intercept form for
the line that contains (8, 2) and is parallel to
y = ⅝x - 4
 Write
and equation in slope-intercept form for
the line that contains (2, -6) and is parallel to
y = 3x + 9
 Perpendicular
Lines = Lines that
intersect to form right angles (90&deg;)
Write an equation in slope-intercept form for both
of the lines below….what do you notice?
y = -(4/3)x + 5
y = &frac34;x + 3
 The
slopes of perpendicular lines are
negative reciprocals of each other.
 Negative

reciprocals:
Ex.


The negative reciprocal of &frac12; is -2.
The negative reciprocal of -&frac34; is 4/3.
 What
is the slope of a line perpendicular to…
y = ⅝x + 5
6x + 8y = 24
 Are
each pair of lines parallel, perpendicular,
or neither?
y = 3x – 8
and
3x – y = -1
 Are
each pair of lines parallel, perpendicular,
or neither?
9x + 3y = 6
and
3x + 9y = 6
 Are
each pair of lines parallel, perpendicular,
or neither?
y = -(5/2)x + 11
and
-5x + 2y = 20
 Write
an equation in slope-intercept form of
the line that contains (1, 8) and is
perpendicular to y = &frac34;x + 1.
```