Frequently Asked Questions
How do you write a line parallel to another line?
Use the same slope. If the reference is y equals m x plus b and you want to pass through (x naught, y naught), the new line is y equals m x plus (y naught minus m times x naught).
What makes two lines parallel?
They share the same slope and never meet (assuming distinct intercepts). Vertical lines are parallel when they share the same form x equals constant.
Parallel versus perpendicular?
Parallel lines share slope. Perpendicular lines have slopes whose product is minus one, that is, slopes are negative reciprocals of each other.
How do you find a line parallel to another through a given point?
Keep the same slope m as the original line and solve for a new intercept using the point: b = y0 − m·x0. The parallel line is y = m·x + b, sharing the slope but with a different intercept.
Do parallel lines always have the same slope?
Yes, on a plane two distinct lines are parallel exactly when their slopes are equal. Vertical lines are the special case: they are all parallel and share an undefined slope.
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