Parallel Lines
What are parallel lines?
- Parallel lines are lines that have the same gradient, but are not the same line
- Parallel lines do not intersect with each other
- You can easily spot that two lines are parallel when they are written in the form , as they will have the same value of (gradient)
- and are parallel
- and are not parallel
- and are not parallel; they are the exact same line
How do I find the equation of a line parallel to another line?
- As parallel lines have the same gradient, a line of the form will be parallel to a line in the form , where is the same for both lines
- If then they would be the same line and therefore not parallel
- If you are asked to find the equation of a line parallel to , you will also be given some information about a point that the parallel line, passes through;
- You can then substitute this point into and solve to find
Worked example
Find the equation of the line that is parallel to and passes through (2,1)
As the gradient is the same, the line that is parallel will be in the form:
Substitute in the coordinate that the line passes through:
Simplify:
Subtract 6 from both sides:
Final answer: