Educator

Parallel Lines and Perpendicular Lines

• Parallel lines are two lines in the same plane that do not intersect. Two non-vertical lines are parallel if and only if they have the same slope.

• If you are given the equation of a line and a point not on that line, you can find the equation of the line through this point parallel to the given line by using the point-slope form.

• Perpendicular lines are lines that intersect at right angles. Two non-vertical lines are perpendicular if and only if the product of their slopes is –1 (or, equivalently, their slopes are negative reciprocals of each other).

• You can use this fact to determine whether a pairs of lines whose equations have been given are perpendicular or not.

• If you are given the equation of a line and a point, you can find the equation of the line through this point perpendicular to the given line by using the point-slope form. You must first find the slope of the given line and then take its negative reciprocal.