Parallel and Perpendicular Lines
5-6
Parallel Lines
• Parallel lines do not intersect!
y = 2x + 4 and y = 2x + 3 will be
parallel.
• Parallel lines will have the same
slope and different y-intercepts.
Parallel Lines
y = 2x + 4
be parallel.
and y = 2x + 3 will
Parallel Lines
• Write the slope-intercept form of an
equation for the line that passes through
(-1,-2) and is parallel to the graph of
y = -3x -2. THE SLOPE OF BOTH
EQUATIONS WILL BE -3.
y = mx + b
(-1,2) SLOPE = -3
-2 = -3(-1) + b
-2 = 3 + b
-3 = -3
- 5 = b
The equation is: y = -3x -5
• Example 2
Write the slope-intercept form of an
equation for the line that passes
through (4,-2) and is parallel to
the graph of y = 1 x -7
2
( The slope will be 1 )
2
Parallel Lines
• Write an equation of the line
containing the point (0,6) and parallel
to the line: The slope will be -3
y = -3x + 4
Perpendicular Lines
• Perpendicular lines intersect and form rt.
angles. The product of the slopes is -1.
• Ex if a slope is -3, then the other slope of
the line is 1
3
BECAUSE:
-3
1
* 1 = -1
3
Perpendicular Lines
• If a slope is -1 the line perpendicular
4
to that line must be 4 because:
-1 * 4 = -4 = -1
4
1
4
Perpendicular Lines
• Write the slope-intercept form of an equation
that passes through (-2, 0) and is
perpendicular to the graph of y = x -6
Slope of equation is 1, New slope must be
-1 because 1 * -1 = -1
1 1
y = x -6
0 = -1(-2) + b
0=2 +b
b = -2
Equation: y = -1x – 2 or y = -x -2
Perpendicular Lines
•
Write the slope-intercept form for an
equation for the line that passes through
(-1,3) and is perpendicular to 2x + 4y = 12
a) Solve for y in terms of x: 2x + 4y = 12
b) Substitute values in for x, y, and m
Practice
•
Write the slope-intercept form of an equation
of the line that passes through the given point
and is ll to the graph of the equation.
1) (3,2), y = 3x + 4
2) (-1,-2) y = -3x + 5
Practice
• Write the slope-intercept form of an equation of
the line that passes through the given point and
is ll to the graph of the equation.
3) (3,2), y = 3x + 4
4) (-5,-1), 2y = 2x -4
Practice
• Write the slope-intercept form of an equation of
the line that passes through the given point
and is perpd.( l ) to the graph of each equation.
5) (-3,-2), y = x + 2
6) (4,-1), y = 2x -4
Practice
•
Write the slope-intercept form of an equation
of the line that passes through the given point
and is l to the graph of each equation.
7) (-5,1), y = - 5 x -7
3
8) (-2,2) 6x + 3y = -9
Guided Practice
• See pg 295 #4