Parallel Lines Examples

What is the defining characteristic of parallel lines?

To be parallel to each other, lines must satisfy two basic characteristics. They must be on the same plane and they must never intersect. That's all there is to it.

What symbol do you use to indicate that CD is parallel to WV?

A double bar in between the two lines. So you could write CD ǁ WV.

How do you indicate that CD and PQ are parallel when drawn?

Use arrows or double arrows within the lines to show that they're parallel. Lines that are parallel to each other should have the same number of arrows.

A line that goes through point (2, 2) is parallel to a line with an equation of 2x – 4y = 12. What is the equation of the second line?

First, we need to get this equation out of its standard form outfit and into something a little more comfortable. If we change 2x – 4y = 12 into slope-intercept form, we'll have the slope right in front of us. We already know algebra, so changing this equation into y = ½x – 3 shouldn't be too big of a deal.

Parallel lines have the same slope (which is ½ in this case), so our second line should have the equation y = ½x + b. The final piece of the puzzle is finding out what that b equals, and we can use the point (2, 2) to do that.

y = ½x + b
2 = ½(2) + b
2 = 1 + b
b = 1

The equation of the line parallel to y = ½x – 3 that passes through (2, 2) is y = ½x + 1. Are we sure the lines are parallel? Both their slopes are ½, so yep. Are we sure the lines are different? Their equations are different, so yep.