Most people say that teaching is the noblest profession and probably the hardest. Because being a teacher is not as easy as to what others think about. Because teachers are molders of the future generation. Teachers especially the effective ones proposed strength and stability to what his or her students would become. The roles of teachers are very important in every human development.

 Thus I can compare teachers to parallel lines and its concepts. Its concepts are needed in order to construct strong and stable high-rise buildings as well as their electrical installations. Not only that. Railways whom engineers always make sure that the rails of the track are always of the same distance apart so that the train’s wheel can run.

Furthermore, there are many real-life examples that can be described by using parallel lines. Railroads, beams of buildings and structures, light rays, the rungs on the ladder are other examples that suggest the use of parallel lines.

What are parallel lines?

Parallel lines are two lines that lie within the same plane and never intersect each other and they have the same slope.

·        Slope (m): The measure of the steepness of a line; it is the ratio of vertical change to horizontal change.

Thus,

Two non-vertical lines are parallel if and only if their slopes is equal.

If l₁║l₂, then m₁= m₂.                                                       
If m₁= m₂, then l₁║l₂.             

·    If the given equation of the line is in slope-intercept form, (y=mx+b) then the line’s slope is the number being multiplied by x.

This means that, we can determine If lines are parallel just by looking at their equations in slope-intercept form.

For example:

y = 3x – 5      and    y = 3x + 2 are parallel.

                 same slope

y = 3x – 1       and   y = 6x + 1 are not parallel.

                 different slope

How to find the equation of the line given the slope and a point?

Example:

Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2

                   m = 2/3 and the point is (3,6)

*Using the slope intercept form,

y = mx+b

6 = 2/3(3)+b

6 = 2+b

4 = b

y = 2/3x+4

                  

*Using the point – slope form,

y – y₁ = m(x – x₁)

y – 6  = 2/3( x – 3 )

3(y-6) = 2x – 6

3y-18 = 2x – 6

 y = 2x + 12    

   3

 y = 2 x + 4      

       3

·        
Therefore, there are two main ways of determining the equation of a line parallel to a line given the slope and a point. We can use the slope-intercept form or point-slope form.

References:

Padua, Ong, Lim-Gabriel, de Sagun and Crisostomo ( 2013 ). Parallel and 

     Perpendicular Lines. Our World of Math, 140-143.

Mathispower4u. Find the Equation of a Line Parallel to a Given Line Passing

     Through A Given Point. https://www.youtube.com/watch?v=TrONIeOpJHg

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