Parallel and Perpendicular Lines

Understanding Parallel Lines

Parallel lines are lines in a plane that do not intersect.
On a graph, parallel lines have identical gradients.
In other words, if line 1’s equation is y = mx + c1 and line 2’s equation is y = mx + c2, then the lines are parallel.
‘m’ is the slope or gradient which is the same for both parallel lines.
‘c1’ and ‘c2’ are different points where the lines intersect the y-axis.
Parallel lines may have different y-intercepts, but the gradient or slope (rate of change of y with respect to x) is the same.

To draw a line parallel to another, choose the same gradient ‘m’ for the new line.
The y-intercept ‘c’ for the new line can be any value, as this will not impact the parallel nature of the two lines.
After identifying ‘m’ and ‘c’, proceed as previously discussed in the section regarding drawing straight line graphs.

Perpendicular lines are lines which meet or intersect at right angles.
In a graph, two lines are perpendicular if the product of their gradients is -1 (negative one).
If line A has gradient m1, and line B has gradient m2, and if m1 * m2 = -1, the lines are perpendicular.

To draw a line perpendicular to an existing one, the gradient of the new line is the negative reciprocal of the gradient of the original line.
If the original line’s gradient is ‘m’, then the gradient of the line perpendicular to it is -1/m.
Choose any suitable point (preferably one that makes calculations easy) on the original line to calculate the y-intercept of the new line.
Once the gradient and y-intercept have been identified, draw the perpendicular line using the techniques for drawing straight line graphs.

Confirm the relationship of the gradients using the product rule mentioned above.
Perpendicular lines should intersect at a right angle. This can be a useful visual check but may not be totally accurate depending on the scale of your graph.
Check a few sets of corresponding points on both lines to ensure the perpendicular nature of the lines.