Lines: Slopes of Parallel and Perpendicular Lines
To find the slope of a line when given the equation of the line:
1)
Write the equation in y  mx  b form (solve for y)
2)
The coefficient of x is the slope m (number in front of x)
Problems:
1)
Find the slope of the line whose equation is y - 3x = 7.
2)
What is the slope of the line whose equation is 2y + x = 7?
3)
What is the slope of the line whose equation is x = 13?
4)
Find the slope of the line whose equation is 2x + 5y = 6.
5)
What is the slope of the line whose equation is 24 = y?
6)
Find the slope of the line whose equation is 3y – 6x = 12
7)
What is the slope of the line whose equation is 3x = 4?
To determine if two lines are PARALLEL:
1)
Find the slope of each line
2)
If the slopes are the same and the y-intercepts are different, the lines are
parallel
To determine if two lines are PERPENDICULAR:
1)
Find the slope of each line
2)
If the slopes are negative reciprocals of each other, the lines are
perpendicular
Problems:
1)
Determine if the pair of lines are parallel, perpendicular or neither:
-4x + 3y = 4
-8x + 6y = 0
2)
Determine if the following pair of lines are parallel, perpendicular or neither:
-6x + 2y = 6
-y = 3x - 2
3)
Determine if the following pair of lines are parallel, perpendicular or neither:
2y + 4x = 10
y - .5x +-3/2 = 0
4)
The lines represented by the equations
1)
2)
3)
4)
and
the same line
parallel
perpendicular
neither parallel nor perpendicular
are
To find the slope of a line, parallel, to a given equation of a line:
1)
Find the slope from the given equation of the line
2)
The slope of the line parallel to the given line will be the same as the slope
of the given line
To find the slope of a line, perpendicular, to a given equation of a line:
1)
Find the slope from the given equation of the line
2)
The slope of a line perpendicular to the given line will be the negative
reciprocal of the slope of the given line.
Problems:
1)
What is the slope of a line that is parallel to the line whose equation is
2)
What is the slope of a line perpendicular to the line whose equation is
3)
Find the slope of a line parallel to the line whose equation is 3x  2 y  10 .
4)
What is the slope of a line that is perpendicular to the line whose equation is
represented by 3 y  6 x  3 ?
5)
Given the equation of line l: x  4 y  12 , (a) find the slope of a line that is
parallel to l (b) find the slope of a line that is perpendicular to l.
?
?