parallel & perpendicular lines parallel lines – have the same slope perpendicular lines –...
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Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to y = 3x - 4
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to y = 3x – 4
The slope of the current line is m = 3
Parallel lines have the same slope so m = 3
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
You must solve for y to get the equation into y = mx + b form
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
You must solve for y to get the equation into y = mx + b form
42
52
8
2
5
2
2
852
55
852
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
You must solve for y to get the equation into y = mx + b form
42
52
8
2
5
2
2
852
55
852
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
You must solve for y to get the equation into y = mx + b form
42
52
8
2
5
2
2
852
55
852
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
You must solve for y to get the equation into y = mx + b form
42
52
8
2
5
2
2
852
55
852
xy
xy
xy
xx
xyParallel lines have the same slope.
So m = 2
5
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to yx 43
2
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
Slope of the given line is
yx 43
2
3
2
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
Slope of the given line is
Perpendicular slope - reciprocal ( flip the fraction ) and opposite sign
yx 43
2
3
2
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
Slope of the given line is
Perpendicular slope - reciprocal ( flip the fraction ) and opposite sign
m =
yx 43
2
3
2
2
3
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to 23 xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
3
2
3
13
2
33
3
23
23
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
3
2
3
13
2
33
3
23
23
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
3
2
3
13
2
33
3
23
23
xy
xy
xy
xx
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
3
2
3
13
2
33
3
23
23
xy
xy
xy
xx
xym of current line =
3
1
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the slope of the line perpendicular to
First solve for y to get equation into y = mx + b form
23 xy
3
2
3
13
2
33
3
23
23
xy
xy
xy
xx
xym of current line =
3
1
1
3m
Flip fraction & change sign
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru
the point ( 2 , 6 )
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru
the point ( 2 , 6 )
Use point – slope form y = m ( x – a ) + b
Parallel m = - 4 and the point ( 2 , 6 ) becomes our ( a ,b )
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru
the point ( 2 , 6 )
Use point – slope form y = m ( x – a ) + b
Parallel m = - 4 and the point ( 2 , 6 ) becomes our ( a ,b )
y = - 4 ( x – 2 ) + 6
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 4 , 7 ) and
is parallel to a line that has a slope of m = 2
1
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 4 , 7 ) and
is parallel to a line that has a slope of m =
Using point – slope form y = m ( x – a ) + b substitute
m and ( a , b )
2
1
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 4 , 7 ) and
is parallel to a line that has a slope of m =
Using point – slope form y = m ( x – a ) + b
2
1
742
1
7)4(2
1
xy
xy
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( 1 , - 4 ) and
is perpendicular to a line with has a slope of m = 6
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( 1 , - 4 ) and
is perpendicular to a line with has a slope of m = 6
4,1 thru 6
1m
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( 1 , - 4 ) and
is perpendicular to a line with has a slope of m = 6
4,1 thru 6
1m
416
1
)(
xy
baxmy ** use point – slope form and substitute m and ( a , b )
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
32
6
2
3
2
2
632
3 3
623
xy
xy
xy
xx
yx Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
32
6
2
3
2
2
632
3 3
623
xy
xy
xy
xx
yx Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
32
6
2
3
2
2
632
3 3
623
xy
xy
xy
xx
yx Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
32
6
2
3
2
2
632
3 3
623
xy
xy
xy
xx
yx Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
3 xy
1,2 thru 3
2
m
Parallel & Perpendicular Lines
Parallel Lines – have the SAME slope
Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
EXAMPLE : Find the equation of the line that runs thru the point ( - 2 , - 1 ) and
is perpendicular to 623 yx
32
3 xy Solve for y and get into y = mx + b form
1,2 thru 3
2
m
123
2
1)2(3
2
xy
xy
baxmy