Parallel Lines
What are parallel lines?
- Parallel lines are lines that have the same gradient
- Parallel lines do not intersect with each other
- You can easily spot that two lines are parallel when they are written in the form ,
- They will have the same value of (gradient)
- and are parallel (and therefore will never intersect)
- and are not parallel (and therefore must intersect)
- They will have the same value of (gradient)
How do I know if two lines are parallel to one another?
- If you are given the equations of two lines, rearrange them into the form if they are not in it already
- If the two lines have the same value for , they are parallel
How do I find the equation of a line that is parallel to another line?
- You may be asked to find the equation of a line parallel to a line of the form
- You will also be given some information about a point that the parallel line, passes through;
- Substitute into the equation, , the value of (this will be the same as for the original line) and the coordinates of the point through which it passes
- Solve the equation formed to find
- Write the equation of the parallel line substituting in the values of and
Worked example
Find the equation of the line that is parallel to and passes through the point (2,1).
As the gradient is the same, the line that is parallel will be in the form
Substitute in the coordinates that the line passes through
Simplify
Subtract 6 from both sides
Write the equation in the form , substituting in the values of and that you have found