This is a free lesson from our course in Algebra I
In this lesson, we introduce parallel and perpendicular lines as well as look at the relationship
between their slopes. Parallel Lines are distinct lines lying in the same plane; they never intersect each other and have the same slope. Two lines Ax + By +
C = 0 and Dx + Ey + F = 0 are parallel if A/D = B/E. For example,
2x + 4y = 5 and 2y + 4x = 6 are parallel lines.
Perpendicular lines are lines that intersect at right angles. If two lines are perpendicular
to each other, then the product of their slopes is equal to 1 i.e. the slopes are
reciprocals of each other with opposite signs. For example,
3x + 4y = 12 and 4x  3y = 20 are perpendicular
lines. (More text below video...)
Another way to look at parallel and perpendicular line is since slope is a measure of the angle of a line from the horizontal
, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope
are parallel. Perpendicular lines are a bit more complicated. If you visualize a line with positive slope (so it's an increasing line),
then the perpendicular line must have negative slope (because it will be a decreasing line). So perpendicular slopes have
opposite signs. The other "opposite" thing with perpendicular slopes is that their values are reciprocals;
that is, you take the one slope value, and flip it upside down. Put this together with the sign change,
and you get that the slope of the perpendicular line is the "negative reciprocal" of the slope of the original line —
and two lines with slopes that are negative reciprocals of each other are perpendicular to each other.
In numbers, if the one line's slope is m = 3/4, then the perpendicular line's slope will be m = –4/3.
If the one line's slope is m = –2, then the perpendicular line's slope will be m = 1/2.
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