This is a free lesson from our course in Algebra I
This lesson explains how to find the equation of a line parallel to another given
line. The steps are simple:
• calculate slope of the given line
• extract other information provided, e.g. the yintercept, a given point on that line etc.
• find the equation of the new line by the combination of the slope and the other
given information.
Properties of parallel line: • if two nonvertical lines are
parallel, then they have the same slope. • if two distinct nonvertical lines have
the same slope, then they are parallel. • two vertical lines are parallel. (More text below video...)
(Continued from above) E.g. Write
an equation of the line passing through (3,2) and parallel to the line with equation
y = 2x + 1.
The equation y = 2x + 1 is in SlopeIntercept Form, with m = 2. So, the slope of
this line is 2. Since our line is parallel to this given line, it must have the
same slope. Therefore, you have to find the equation of a line with slope 2 passing
through the given point (3,2).
PointSlope
Form: y – y1 = m(x x1)
y 2 =2(x  (3))
Substitute: m = 2,
y – 2 = 2(x + 3)
Simplify, y – 2 = 2x + 6
y = 2x + 8
Solve for y,The equation of the line is y = 2x + 8.
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