*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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