Parallel Lines

Key points

Parallel lines are two lines that will never meet, and run alongside each other without ever getting any closer.
Parallel lines must have the same gradient/slope and different y-intercepts.

Parallel Lines are lines that run adjacent each other without ever intersecting. They never get any closer.

They must have the same slope/gradient.
- If their rate of change, or “steepness” is different, then they will meet at some point.
- This applies with any slope – positive, negative, zero, or undefined.
The y-intercepts of parallel lines must be different.
- If they have the same slope and y-intercept, then they are the same line.
- A different y-intercept with the same slope means they infinitely run adjacently without getting closer.
In this example, the lines both have a slope of 3/4, but one has a y-intercept of (0,1), and the other (0,-3).