Parallel Line Equation - Math, Class 10 Video Lecture

Write the equation of
a line that is parallel
to line 2x minus
4y is equal to 8
and goes through the point 3, 0.
So because this line is parallel
to this right over here,
that just means that it
has the exact same slope.
So it's essentially
saying, find the equation
of a line that has the
same slope as this line
and goes through this point.
So first, let's figure out
what the slope of this line
is, and the easiest
way to do that is
to put this in kind of
slope, y-intercept form.
So we have 2x minus
4y is equal to 8.
We want to solve
for y, we want this
to be in the form y
is equal to mx plus b.
So let's add-- even
better, let's subtract 2x
from both sides, so we can
isolate the y's on the left.
So that cancels out.
And we have negative 4y is
equal to negative 2x plus 8,
and I'm writing the
negative 2x first
just because that gets us
closer to the mx plus b form.
Now, we could divide both sides
of this equation by negative 4
so we can isolate the y.
So we divide everything
by negative 4,
and the left hand side, we
just have a y is equal to
and negative 2 divided
by negative 4 is 1/2.
So y is equal to 1/2x, and
then 8 divided by negative 4
is negative 2.
So we could write
plus negative 2
or we could just write minus 2.
So we just rewrote
this line over here,
but because we wrote
it in mx plus b form,
we now know its slope.
The slope of this line is 1/2.
That right there is the slope.
So the equation of the
line that we care about
is going to have the same slope.
It's going to have the
form y is equal to 1/2
x plus some y-intercept.
It's not exactly
this line. b is going
to be different than
this negative 2 here,
but b is going to
have the same slope.
They're going to intersect the
y-axis in a different place,
but they're going to be
parallel to each other.
So now, we need to figure
out how to figure out b.
And to do that we have this
information right over here.
On this line, the one we care
about, when x is 3, y is 0.
When x is 3, y is equal
to 0, or we could say 0
is equal to 1/2 times 3 plus b.
We just have to find a b
that sets up this equation so
that when x is equal
to 3, y is equal to 0.
So we get 0 is
equal to 3/2 plus b.
Subtract 3/2 from both sides,
and we get negative 3/2
is equal to b, or b is
equal to negative 3/2.
So we have the
equation for our line
that is now parallel to this
equation, and goes to the point
3 comma 0.
It is y is equal to-- it has
the same slope as this guy
up here, 1/2x, and now we know
its y-intercept, minus 3/2.
And we are done.
And actually, if
you're interested,
you could graph these two and
see that they're parallel.
So if you were to
graph these-- I'll
do just a very rough
graph really fast.
So this is my y-axis.
This is my x-axis.
This line up here,
I'll do in blue,
which is the same thing as
this line right over here.
I just algebraically
manipulated it.
It has a y-intercept
at negative 2.
So negative 2.
So 1, 2, at negative 2,
and has a slope of 1/2.
So that means that for
every one it goes over,
it only goes 1/2 up, or
for every 2 it goes over,
it only goes 1 up.
So it's going to look
something like this.
I'll try my best to draw it.
It's going to look
something like that.
And so this line over here, its
y-intercept is at negative 3/2,
and negative 3/2 is the same
thing as negative 1 and 1/2,
so it's going to
be right over here.
So it's going to
be right above it.
Right over there and it's going
to have the exact same slope.
So it's going to
be right above it.
It's going to be parallel.
Right above it, just like that.
I'll do my best
to draw parallel,
and so it would look like that.
They're parallel, but
they're different lines
because they have
different y-intercepts.