Download 6-6 PARALLEL AND PERPENDICULAR LINES

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PARALLEL AND
PERPENDICULAR LINES
1) Write an equation of the line that passes through a
given point, parallel to a given line.
2) Write an equation of the line that passes through a
given point, perpendicular to a given line
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Parallel lines:
Lines that never intersect
The symbol for
parallel lines is: ││
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If two lines are parallel that
means they have
THE SAME SLOPE!!!
Examples:
1) A line that is parallel to y = 5x -2 will have a slope of ________.
2) A line that is parallel to y = -3x+4 will have a slope of _______.
3) A line that is parallel to y = ½ x -1 will have a slope of_______.
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1)
2)
In order to determine if two lines are parallel
we need to put both equations into slope
intercept form (y=mx+b).
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3)
4)
In order to determine if two lines are parallel
we need to put them into slope intercept form
(y=mx+b)
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Write equations of lines that are parallel to a
given equation and go through a specific point.
STEPS:
1. Plug in the SAME slope into y = mx +b
– Because parallel lines have the same slope
2. Plug in the x and y value given and solve for b.
3. Rewrite your answer as y = mx + b
Write an equation in slope-intercept form of the
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line that passes through the given point and is
PARALLEL to the graph of each equation.
5)
Goes through (12, 3) and is parallel to: y = 2x + 5
Write an equation in slope-intercept form of the
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line that passes through the given point and is
PARALLEL to the graph of each equation.
6)
Goes through (4, –2) and is parallel to: y= ½x-7
Write an equation in slope-intercept form of the
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line that passes through the given point and is
PARALLEL to the graph of each equation.
7)
Goes through (-1, -4) and is parallel to: 3y = -9x + 8
Write an equation in slope-intercept form of the
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line that passes through the given point and is
PARALLEL to the graph of each equation.
8)
Goes through ( 0, 4) and is parallel to: x + 5y = 4
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Perpendicular Lines:
Lines that intersect at a right angle (90o angle).
The symbol for perpendicular lines is:
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Perpendicular lines have slopes that are:
OPPOSITE RECIPROCALS!
+
−
FLIP THE SYMBOL!
a
b
b
a
FLIP THE NUMBERS!
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Find the OPPOSITE RECIPROCAL
1. The opposite reciprocal of 2 is________
2. The opposite reciprocal of (1/3) is _________
3. The opposite reciprocal of (3/4) is ______
4. The opposite reciprocal of 5 is _______
5. The opposite reciprocal of (1/4) is ______
6. The opposite reciprocal of (6/7) is _________
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7)
8)
In order to determine if two lines are
perpendicular we need to put them into slope
intercept form (y=mx+b)
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9)
10)
In order to determine if two lines are
perpendicular we need to put them into slope
intercept form (y=mx+b)
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Write equations of lines that are perpendicular to
a given equation and go through a specific point.
STEPS:
1. Plug in the OPPOSITE RECIPROCAL slope into
y = mx +b
– Because perpendicular lines have slopes that are
opposite reciprocals.
2. Plug in the x and y value given and solve for b.
3. Rewrite your answer as y = mx + b
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Write an equation in slope-intercept form of the line
that passes through the given point and is
PERPENDICULAR to the graph of each equation.
11)
Goes through (2, 3) and is perpendicular to: y = 2x + 3
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Write an equation in slope-intercept form of the line
that passes through the given point and is
PERPENDICULAR to the graph of each equation.
12)
Goes through (1, 1) and is perpendicular to: y = -4x + 1
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Write an equation in slope-intercept form of the line
that passes through the given point and is
PERPENDICULAR to the graph of each equation.
13)
Goes through (-2, 7) and is perpendicular to: -5y = -2x +3
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Write an equation in slope-intercept form of the line
that passes through the given point and is
PERPENDICULAR to the graph of each equation.
14)
Goes through (4, –1) and is perpendicular to: 7x – 2y = 3.