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
moulders 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.
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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 are 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
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