Parallel and Perpendicular Lines
Parallel and perpendicular lines are two types of lines that are important to understand in algebra. Parallel lines are lines that never intersect, while perpendicular lines are lines that intersect at a right angle (90 degrees). Whether lines are parallel or perpendicular depends on their slopes.
Parallel Lines
Parallel lines have the same slope. For example, the lines y = 3x + 2 and y = 3x - 1 are parallel because they have the same slope of 3. Two parallel lines will never intersect, and will always be the same distance apart. If you can show that two lines have the same slope, you can conclude that they are parallel.
Perpendicular Lines
Perpendicular lines have slopes that are negative reciprocals of each other. A reciprocal of a number is the result of dividing 1 by that number, or flipping the numerator and denominator. For example, the reciprocal of 3 is 1/3, and the reciprocal of -5/6 is -6/5. A negative reciprocal is where you not only take the reciprocal, but also multiply by -1. For example, the negative reciprocal of 3 is -1/3, and the negative reciprocal of -7/8 is 8/7. If you can show that two lines have slopes that are negative reciprocals of each other, you can conclude that they are perpendicular.
Finding the Equation of a Perpendicular Line
If you have an equation for a line and a point on that line that a perpendicular line passes through, you can find the equation of the perpendicular line by following these steps:
- Find the slope of the original line.
- Find the negative reciprocal of the slope.
- Use the point-slope form of the equation of a line to find the equation of the perpendicular line.