Perpendicular and Parallel Lines

Front

What are the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are opposite reciprocals.

Front

If a line has a slope of -2/3, 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 -2/3 is 3/2.

Front

What is the slope of a line parallel to a line with a slope of 3/7?

Back

The slope of a line parallel to a line with a slope of 3/7 is also 3/7.

Front

How do you write the equation of a line perpendicular to y = 2x + 3 through the point (-2, 4)?

Back

To write the equation, first find the slope of the perpendicular line, which is -1/2. Then use point-slope form: y - 4 = -1/2(x + 2), which simplifies to y = -1/2x + 3.

Front

What is the equation of a line that is perpendicular to y = 3x - 6 and passes through the point (15, 5)?

Back

The slope of the line perpendicular to y = 3x - 6 is -1/3. Using point-slope form: y - 5 = -1/3(x - 15), which simplifies to y = -1/3x + 10.

Front

What is the definition of parallel lines?

Back

Parallel lines are lines in a plane that never meet; they have the same slope.

Front

What is the definition of perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees); their slopes are opposite reciprocals.

Front

How can you determine if two lines are parallel using their equations?

Back

Two lines are parallel if their slopes are equal.

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the slope-intercept form of a line?

Back

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