Parallel lines are two lines that never cross. On a graph they would resemble a pair of train tracks. They will have the same slope and different y-intercepts. The reason they have different y-intercepts is because if they had the same y-intercept they would then be the same line.

 

Perpendicular lines are lines that meet at 90° angles. Do not worry about their y-intercepts, only their slope. Perpendicular lines have slopes that are opposite reciprocals. Opposite reciprocals are numbers that are opposite in sign and “flipped over.” For example, if one is looking for the opposite reciprocal of it would be . Say one wants to find the opposite reciprocal of 5. Since 5 is the same as , the opposite reciprocal is . Here is a list of a few numbers and their opposite reciprocals.

 

Number Opposite Reciprocal

 

-6

 

-3

 

Find the opposite reciprocals when comparing slopes to see if two lines are perpendicular.

Example

 

Is the following pair of lines parallel, perpendicular, or neither?

y = 3x -4

 

y = 3x +7

 

Look at their slopes, 3 and 3. Since they are the same, these two lines are parallel.

Parallel

 

Answer!

 

 

 

 

 

 

Example

Is the following pair of lines parallel, perpendicular, or neither?

y = x

 

y = x +2

 

Look at their slopes, and . These are opposite reciprocals therefore these lines are perpendicular.

 

 

Perpendicular

 

 

Answer!

 

 

 

 

 

 

 

Example

Is the following pair of lines parallel, perpendicular, or neither?

y = x

 

y = x +2

 

 

Looking at their slopes one can tell that they are reciprocals but not opposites. Since they are not equal or opposite reciprocals these two lines are neither parallel nor perpendicular.

Neither

 

Answer!