Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet or intersect. 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 perpendicular lines are opposite reciprocals.

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, and is calculated as the rise over run.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

If two lines are parallel, what can you say about their slopes?

Back

The slopes of parallel lines are identical.

Front

If two lines are perpendicular, what can you say about their slopes?

Back

The slopes of perpendicular lines are opposite reciprocals.

Front

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

Back

The equation is y = 3x + 1.

Front

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

Back

The equation is y = rac{1}{2}x + 0.

Front

How do you determine if two lines are parallel or perpendicular from their equations?

Back

Compare their slopes: if slopes are equal, lines are parallel; if slopes are opposite reciprocals, lines are perpendicular.