How to tell if lines are parallel, perpendicular or neither?

Parallel lines are the lines that never intersect and perpendicular lines are the lines that intersect at 90 degrees.

Answer: Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.

Let's see how to identify parallel and perpendicular lines.

Explanation:

Let's take some examples to understand this.

Parallel lines:

Considering two equations:

y = 2x +3 and y = 2x+5 

On comparing y = 2x +3 and y = 2x+5 with y = mx + c

Both the lines have the same slope, m = 2, and we know that,

Lines with the same slope are parallel.

Hence, the given lines are parallel.

Perpendicular lines:

Let's consider another set of equations.

y = 2x +3 and 4y = –2x+10

On comparing y = 2x +3 and 4y = –2x+10 with y = mx + c 

The slopes are m = 2 and m = –1/2

If the slope of one line is the negative reciprocal of the second line, then lines are perpendicular.

Hence, both the lines are perpendicular.

Therefore, lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then the lines are perpendicular, otherwise, the lines are said to be just intersecting lines.