Lines are the greatest thing ever to be created. JUST KIDDING. No, I'm serious, l think they are pretty cool. Guess what? There are different kinds of lines. There are food lines, waiting lines, hair lines, finish lines, and straight lines. In graphs and equations there are two different types of lines that can be noticed. The two types of lines are perpendicular and parallel.
On this page, it is all about parallel lines. Parallel lines are the same distance apart, and they will never meet or touch.
Here are some examples of parallel lines:
Horizontal-parallel-lines.jpg
Horizontal Parallel Lines
imagesCA8V3I6H.jpg
Vertical Parallel Lines (Train tracks)
slope_parallel.gif
Parallel Lines on a graph

Y=mx+b is the slope-intercept form. X and Y are the coordinates, m is the slope, and b is the y-intercept

Parallel lines always have to have the same slope in equations in order to never touch and be parallel. You can look at the coefficient of the x variable to see if they have the same slope. The y-intercept, (the b variable) does not affect whether or not the lines will be parallel. It is all about the slope.

Examples-
Ex. 1)
Are these two line parallel to each other
Y=2X-1
Y=2X+3

To see if these two equations are parallel, you have to find the slope of both equations. The slope is the coefficient of X so in both equations, the slope would be 2. Since, both equations have the same slope, the two lines are parallel.

Ex. 2)
What line is parallel to the line of Y=5x+12 and crosses through the point of (4,2)?

-Since the eqaution of y=5x+12 is already in slope-intercept form, you don't need to change anything.
-Since the line also crosses through (4, 2), they are your x and y variables.
-Also, you know that if two lines are parallel, they have to have the same slope. This slope in the first line is 5, so the new line's slope must be 5 too.
-Now, you have the x and y variables, and the slope, so all you have to do is solve for b.
-Plug in all the numbers you found in the slope-intercept form of y=mx+b and solve.
-So the new equation would be
2=5(4) +b
2=20+b
-18=b
-Now that you have found b, write the equation with only the slope and the y-intercept for the line.
Y=5x-18.
Yay!


Graphing
Graphing parallel lines are pretty easy to do, and they are easy to check too.

Let's graph the parallel lines of Y=(1/2)X+2 and Y=(1/2)X+1

-To graph parallel lines, first make sure that the equations are in the slope-intercept form and they are indeed parallel lines, with the same slope.
Y=(1/2)X+2 √
Y=(1/2)X+1√
-Once you have checked everything, we can finally get to the fun stuff

-Graph the lines just like you would graph a regular line.
- But in case you forgot how to graph a line, that's what we're here for!
-First, find the y intercept, if there is one. The y-intercept is the b variable.
Y=(1/2)X+2 So the y intercepts are (0,2) and (0,1)
Y=(1/2)X+1
-Then start plugging in some numbers for X.
Lets plug in the number 7 because everyone loves that number.
-Substitute 7 for X in both equations so they would become
Y=(1/2)(7)+2
Y=(1/2)(7)+1
-Then solve the equations for y
Y=(1/2)(7)+2 =5.5
Y=(1/2)(7)+1 =4.5
Now you have a point for each equation. the points are (7, 5.5) and (7, 4.5)
-Plot the coordinate points.
-Now, you can either connect the dots of the point and its corresponding y-intercepts, or you can plot more points to determine the line.
-But you don't need to plot more points because parallel lines are always straight.
The resulting graph should look like this...
external image parallel-lines.jpg




Parallel lines, equations and graphs are all pretty easy to understand. Basically, just remember that in order to have parallel lines you must have:
-same slope
-lines NEVER intersect

That is it. Now you know all about parallel lines and how they are created through different equations, slopes, and graphs.
And don't forget to credit us when you ace your tests! (And don't mention us if you fail.)