Parallel and Perpendicular Slopes

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 change in y divided by the change in x (rise/run).

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, regardless of how far they are extended.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that one slope is the negative reciprocal of the other.

Front

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

Back

The slope of a line that is perpendicular to a line with a slope of 2 is -1/2.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope of the line is 4.

Front

If two lines have slopes of 3 and -1/3, what can we say about their relationship?

Back

The two lines are perpendicular because the product of their slopes (3 * -1/3) equals -1.

Front

What is the slope of the line represented by the equation y = -5x + 2?

Back

The slope of the line is -5.

Front

If two lines are parallel, what can we say about their y-intercepts?

Back

The y-intercepts of parallel lines can be different; only their slopes must be identical.

Front

Given the slopes m1 = 1/2 and m2 = 2, are the lines parallel, perpendicular, or neither?

Back

The lines are neither parallel nor perpendicular because the product of their slopes (1/2 * 2) does not equal -1.

Front

What is the equation of a line that is parallel to y = 3x + 4 and passes through the point (1, 2)?

Back

The equation of the line is y = 3x - 1.