Parallel lines are different lines in the same plane that do not intersect. Parallel lines have the same slope.
Examples of parallel lines:
Example:
Determine if the following lines are parallel.
line 1: y = -3x + 2
line 2: 3x + y = -4
Solution:
First, write each equation in slope-intercept form.
line 1: y = -3x +2
line 2: y = -3x -4
Find the slope of each line.
line 1: m = -3
line 2: m = -3
The slopes are equal and that means that the lines are parallel.
Perpendicular lines:
Two different nonvertical lines in the same plane with slopes m1 and m2 are perpendicular if and only if m2 is the negative reciprocal of m1.
Example of perpendicular lines:
Example:
Determine if the following lines are perpendicular.
line 1: 3x + y = 4
line 2: x - 3y = 6
Solution:
First, write each equation in slope-intercept form.
line 1: y = -3x + 4
line 2: y = 1/3 x - 2
Find the slope for each line.
line 1: m = -3
line 2: m = 1/3
Notice that the slope of line 2 is 1/3 and that its negative reciprocal would be -3/1 which is equal to the slope of line 1. Therefore the lines are perpendicular.
Assignment:
Determine if the following pairs of lines are parallel, perpendicular, or neither.
1. y = 2x - 6 and y = -2x +3
2. x + y = 6 and x - y = 8
3. 2x + y = 3 and 3x - y = 8
4. y = x + 4 and y = x - 9
5. 7x -5y = -18 and 7x - 5y = 21
6. y = 0.5x + 6 and y = -2x + 3
7. 3x - y = 8 and 3x + y = 6
8. 2x - 3y = 5 and 2x - 3y = 8
9. 4x - y = 3 and x + 4y = 6
10. 3x + 2y = 5 and 2x + 4y = 6
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