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 two 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-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

What is the slope of the line y = 3/2x + 3?

Back

The slope of the line y = 3/2x + 3 is 3/2.

Front

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

Back

The equation is y = 3/2x - 2.

Front

What is the equation of a line perpendicular to y = -6x + 2?

Back

The equation is y = 1/6x + 4.

Front

If two lines have slopes of 2 and -1/2, are they parallel, perpendicular, or neither?

Back

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

Front

What does it mean for lines to be neither parallel nor perpendicular?

Back

Lines are neither parallel nor perpendicular if they intersect at an angle that is not 90 degrees and do not have the same slope.