What Are Parallel Lines Definition Equations Examples

today we discuss parallel lines we'll learn the definition equations and look at some examples let's begin parallel lines are two or more lines that are the same distance apart never merging and never diverging we recall that lines are never ending so parallel lines continue forever in two directions always the same distance apart single existing line can have an infinite number of parallel lines too simply by picking point not on any existing line and constructing line parallel to all the existing ones to be two parallel lines both lines must exist in the same plane this differentiates them from skew lines which exist in three dimensions two separate planes parallel lines are by themselves very interesting but when you take segments of them you can construct many polygons think of squares parallelograms rectangles and trapezoids they all have parallel sides to symbolize parallel lines in Geometry we use two upright or slightly slanted lines like this both of those statements tell us that line is parallel to line constructing parallel lines can be done with straight edge pencil and plain paper if using ruler this is one-step process lay the ruler on the paper holding it carefully so it does not slip Trace each edge of the ruler you're done move the ruler and you have parallel lines you can label them identifying each line with two named points and placing arrow heads at the end of the two lines you can also construct line parallel to an existing line passing through single point not on the line pause the video and follow the steps in the how to construct parallel line section of the article below to try it out yourself you'll need drawing Compass plus the plain paper pencil and straight edge now let's look at graphing parallel lines in coordinate graphing parallel lines are easy to construct using the grid system simple equation can provide all the information you need to lay out line 3x - = -4 our line is established with the slope intercept form = * + so we solve the first equation so it is changed to the slope intercept form subtract 3x from both sides simplify divide both sides by -1 and you get = 3x + 4 four now add another line that keeps the value the same you only need to retain 3x so you could write = 3x - 5 this new line is far to the right of the first line but is exactly parallel because the value determined its slope same value same slope both lines parallel