Parallel and Perpendicular Slopes

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm'. It is calculated as the ratio of the rise (change in y) over the run (change in x).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

If the slope of one line is m = 2, what is the slope of a line that is perpendicular to it?

Back

The slope of a line that is perpendicular to m = 2 is m = -1/2, which is the opposite reciprocal.

Front

What are opposite reciprocals?

Back

Opposite reciprocals are two numbers whose product is -1. For example, if one slope is 3, the opposite reciprocal is -1/3.

Front

If two lines have slopes m = 1/2 and m = 1/2, what is their relationship?

Back

The two lines are parallel because they have identical slopes.

Front

What is the slope of a line parallel to m = -3?

Back

The slope of a line parallel to m = -3 is also m = -3.

Front

If the slopes of two lines are m = 4 and m = -1/4, what is their relationship?

Back

The two lines are perpendicular because the product of their slopes is -1 (4 * -1/4 = -1).

Front

What is the slope of a line that is perpendicular to m = 5?

Back

The slope of a line that is perpendicular to m = 5 is m = -1/5.

Front

How can you determine if two lines are neither parallel nor perpendicular?

Back

If the slopes of the two lines are different and do not satisfy the condition for perpendicularity (their product is not -1), they are neither parallel nor perpendicular.