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# Parallel lines from equation (example 2)

Sal determines which pairs out of a few given linear equations are parallel. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

We have three lines and we have
to figure out which of the three are parallel. So line A-- and it can't be
parallel on its own, it has to be parallel to another
of the three lines. So the equation for line
A is y is equal to 3/4 x minus four. Line B is 4y minus 20 is
equal to negative 3x. And then line C is negative
3x plus 4y is equal to 40. So to figure out if any of these
lines are parallel to any of the other lines,
we just have to compare their slopes. If any two of these lines have
the same slope and they're different lines, they have
different y-intercepts, then they're going to be parallel. Now line A, it's very easy
to figure out its slope. It's already in slope-intercept
form. This is mx plus b, the slope
is 3/4 and the y-intercept, which isn't as relevant when
you're figuring out parallel lines, is negative 4. So let's see what the other
character's slopes are. This isn't in any kind
of standard form. It's not a standard form,
slope-intercept, or point-slope form, but let's
see what the slope of this line is. So to get it into
slope-intercept form, which is really the easiest one to pick
out the slope from, let's add 20 to both sides of
this equation. The left-hand side, those cancel
out, that was the whole point, you get 4y is equal
to negative 3x plus 20. And now we can divide
everything by 4. We are left with y is equal
to negative 3/4 x plus 5. So in this case, y-intercept
is 5, but most importantly, the slope is negative 3/4, so
it's different than this guy. This is negative 3/4, this is
positive 3/4, so these two guys definitely aren't
parallel. Let's move on of this guy
in standard form. So let's get the x term
on the other side. So let's add 3x to both sides
of this equation. Left-hand side, these
cancel out. We're just left with 4y is equal
to 3x plus 40, or 40 plus 3x, either way. Now we can divide both sides
by 4 you have to divide every term by 4. The left-hand side, you're
left with y. The right-hand side, you
have 3/4 x plus 10. So here, our slope is 3/4 and
our y-intercept, if we care about it, is 10. So this line and this line have
the exact same slope, 3/4, and they're different
lines because their y-intercept is different. So we know that A and C are
parallel lines and B is not parallel to either one
of the other two.