Parallel Lines Meet

Introduction to parallel lines:

The lines are the straight curve that never ends. We are having two numbers of lines. They are parallel lines as well as perpendicular lines. The distance of the two parallel lines is always the same. They should not meet at any point. When the two lines should meet at a place which should not be  parallel.


More about Parallel Lines:

The parallel lines are represented in pictorial form should be shown below:

One more example for parallel lines that must not meet.

In first diagram, we are having the three lines named as line A, line B and line C. The distance between the line A and line B should not be changed often. They are always in the same distance only but never meet. This is same for the distance between line B and line C as well as line A and line C.

The parallel lines could never meet at any point. Therefore, there is no meeting point for the lines that are in parallel.

Slope of parallel lines:

The parallel line is having same distance apart. Therefore, the slope of the parallel lines could be equal.

Let us consider, the two lines line X and line Y are in parallel. Then, their slope will be equivalent.

That is, Slope of line X = slope of line Y.

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Example Problem:

Check whether the two equations are in parallel. x-2y+5=0 and x-2y+9=0

Solution:

Equation 1: x-2y+5=0

Subtract 5 on both sides, we get, x-2y = -5

Subtract x on both sides, -2y = -x-5 => -2y = -(x+5)

=>  2y = x+5

Divide 2 on both sides, y = `(x)/(2)` + `(5)/(2)`

y = `(1)/(2)` x + `(5)/(2)`

Therefore, slope = `(1)/(2)`

Equation 2: x-2y+9=0

Subtract 9 on both sides, x-2y = -9

Subtract x on both sides, -2y = -x-9 = - (x+9)

2y = x + 9

Divide 2 on both the sides, y = `(x)/(2)` + `(9)/(2)`

y = `(1)/(2)` x + `(9)/(2)`

Thus, the slope = `(1)/(2)`

The slope of both the equations is in equal.

So, the two lines should be in parallel.