Introduction to algebra of parallel lines

Introduction to algebra  of parallel lines:

Definition of parallel lines:

The algebra parallel lines do not intersect each other.
Standard form of equation of a line is
                      y = mx + c

           Y = m1 x + c ---- equation of line 1

           Y = m2 x + c ---- equation of line 2

           M1 = slope of line 1

           M2 = slope of line 2

  Slope of lines must be same for the lines to be parallel.
   The condition of a line to be parallel m1 = m2

Concept of Parallel Lines :

 The two distinct lines have a common point, then the lines are called intersecting lines. If the two distinct lines in a plane have no point in common that is intersecting, then the two lines are called non-intersecting lines. Two non-intersecting lines are also called as parallel lines.

Algebra Parallel Lines:examples

1. Y = 4x + 64, 4y = 6x + 1 identify the two lines are parallel or not.

Solution:Condition for the two lines to be parallel the slope of lines must be same

The standard form of the equation of line is   

                              Y = mx + c

By comparing the first equation with the standard form, we get slope of line1 (m1) = 4.

By comparing the equation 2 with the standard form we get the slope of the line2 (m2) = 3/2.

 As per the condition for parallel line m1 must be equal to m2.Here the m1 is not equal to m2.

The two lines are not parallel. The slopes of two lines are not same so the two lines are not parallel lines.

2.Y = 4x + 6, 4y = 16x + 12 identify the two lines are parallel or not.

Solution:Condition if the two lines to be parallel line the slope of lines must be same or equal

The standard form of the equation of line is

                             Y = mx + c

By comparing the first equation with the standard form, we get slope of line1 (m1) = 4.

By comparing the equation 2 with the standard form we get the slope of line1 (m2) = 4

As per the condition for parallel line we get it as m1 = m2.

                                   4 = 4

The slopes of two lines are same so the two lines are parallel lines.