Parallel & Perpendicular Lines in coordinate Geometry

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Transcript Parallel & Perpendicular Lines in coordinate Geometry

PARALLEL & PERPENDICULAR LINES IN
COORDINATE GEOMETRY
What
types of slopes do parallel
lines have?
What
types of slopes do
perpendicular lines have?
Parallel
lines have the same
slope.
Perpendicular
lines have slopes
that are opposite reciprocal.
ANSWER THE FOLLOWING QUESTIONS
WITH YOUR GROUP MEMBERS




What is the slope of a line parallel to y = 3x – 7?
What is the slope of a line perpendicular to
y = -2x + 6?
What is the slope of a line parallel to y = 9?
What is the slope or a line perpendicular to
y = -x/5 + 11
Find
the equation of a line that
is parallel to the line y = -7x + 4
and passes through the point
(-4, 6)
STEP ONE
Identify
the slope and point
 Slope is -7
 Point is (-4, 6)
If we have a point and a slope, what form of an
equation do we need to use?
STEP TWO
Plug
into point – slope form
 y – y1 = m(x – x1)
y
– 6 = -7(x – -4)
STEP THREE
Finish
by putting equation into
slope-intercept form
y
– 6 = -7(x – -4)
y – 6 = -7(x + 4)
y – 6 = -7x – 28
y = -7x – 22
Find
the equation of a line that
is perpendicular to the line
y = 3x – 9 and passes through
the point (-1, 8)
STEP ONE
Identify
the slope and point
1
 Slope is  3
 Point is (-1, 8)

If we have a point and a slope, what form of an
equation do we need to use?
STEP TWO
Plug
into point – slope form
 y – y1 = m(x – x1)
y
– 8 = (x – -1)
1
y – 8 = x – 3
1
3
1

3




STEP THREE
Finish
by putting equation into
slope-intercept form
y
– 8 = (x – -1)
 y – 8 = (x + 1)
1

y – 8 = x – 3
26
  1
y = 3 x + 3

1
3
1

3
1

3


TRY ON YOUR OWN!!!
 Find
the equation of a line that is
perpendicular to the line y = -2x – 9 and
passes through the point (-4, 6)
 Find
the equation of a line that is parallel
to the line y = 3x + 5 and passes through
the point (-9, 1)
TIME TO PROCESS WHAT YOU
LEARNED




THINK TO YOURSELF!!!
Think of a three word statement that sums up something
you learned from this lecture.
DO NOT SAY IT OUT LOUD!!!
We will go around the room and share in two
minutes