Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. 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 perpendicular lines are negative reciprocals of each other.

Front

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

Back

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

Front

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

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 y = 3x - 12?

Back

The slope of the line y = 3x - 12 is 3.

Front

Write the equation of a line that is perpendicular to y = 2x + 5 and passes through the point (1, 2).

Back

The equation is y = -1/2x + 2.5.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other.

Front

If two lines have equations y = 4x + 1 and y = 4x - 3, are they parallel, perpendicular, or neither?

Back

They are parallel because they have the same slope of 4.