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 but different y-intercepts.

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

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope. For example, if the equations of the lines are in the form y = mx + b, then they are parallel if m is the same for both.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope of m, the other must have a slope of -1/m.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2.

Front

What is the slope of a line that is perpendicular to a line with a slope of 4?

Back

The slope of a line that is perpendicular to a line with a slope of 4 is -1/4.

Front

What is the equation of a line parallel to y = 3x + 1 that passes through the point (2, 5)?

Back

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

Front

If two lines are represented by the equations y = 2x + 1 and y = -rac{1}{2}x + 3, are they parallel, perpendicular, or neither?

Back

They are perpendicular because the product of their slopes (2 and -1/2) is -1.

Front

What is the equation of a line parallel to y = -rac{3}{4}x + 2?

Back

Any line of the form y = -rac{3}{4}x + b, where b is any real number, is parallel.

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal.