Day 6

Parallel and Perpendicular Lines

EMAT6690

by Chris Reid

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