Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet or intersect, no matter how far they are extended. They have the same slope.

Front

What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees). The slopes of two perpendicular lines are negative reciprocals of each other.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run.

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope. If m1 = m2, then the lines are parallel.

Front

How do you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1. If m1 * m2 = -1, then the lines are perpendicular.

Front

What is the negative reciprocal of a slope?

Back

The negative reciprocal of a slope 'm' is -1/m. For example, if m = 2, the negative reciprocal is -1/2.

Front

If the slope of line #1 is 3, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to line #1 with slope 3 is -1/3.

Front

If the slope of line #1 is 5, what is the slope of a line parallel to it?

Back

The slope of a line parallel to line #1 with slope 5 is also 5.

Front

What happens if two lines have the same slope but different y-intercepts?

Back

If two lines have the same slope but different y-intercepts, they are parallel lines and will never intersect.

Front

What is the relationship between the slopes of two lines that are neither parallel nor perpendicular?

Back

If two lines are neither parallel nor perpendicular, their slopes do not satisfy the conditions for either relationship (i.e., they are not equal and their product is not -1).