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.