>> Alright we're going to find
out how to find the x
and y intercepts of a line.
So if you have a graph
of the line you can just look
and see where the line crosses
the x axis
and that would be the
x intercept.
And where it crosses the y
axis and that
that would be the y intercept,
unless it's a vertical
or a horizontal line
in which case there might not
be one of those.
Okay so the first thing we're
going to notice if we look
at a graph,
that all ordered pairs
on the x axis, so if you look
at the x axis I have three
ordered pairs.
Negative five zero, one zero
and three zero.
Notice that all
of the ordered pairs
on the x axis have zero
for its y coordinate.
So an x intercept is
of the form.
Well there's some number
in here for x,
but then the y coordinate will
be zero and now let's look
at the y axis.
I have three ordered pairs.
Zero three, zero one
and zero negative four.
And they all have zero
for their x coordinate right.
So y intercepts are
of the form,
well there's a zero in for x
and then some number for y.
So we're going to use
that idea to figure
out the x intercept
and y intercept of the line
if we know the equation
of the line.
Alright so x intercepts are
on the form something zero.
So we're not sure what the x
is going to be,
that's what we're going
to be looking for,
but note that y equals zero
in the ordered pair.
And for the y intercept there
is zero in for the
x coordinate.
Alright so here's the problem.
Find the x and y intercepts
on the line 3x minus 2y
equals 12.
Okay so let's find the x
intercept first.
Well for the x intercept,
what do we know?
We know half the answer.
We know that the y
coordinate's going to be zero.
So you know half your answer,
put in zero for y right away.
So remember we're trying
to find the x coordinate
here right.
We already know the
y coordinate.
So if we take this equation 3x
minus 2y equals 12
and to get an ordered pair you
have to put in one value for x
to figure out y or vice versa.
We're going to let put in zero
for y. Okay so you're going
to let y equal zero
in this equation.
So we have 3x minus two times
zero equals 12,
which gives me 3x minus zero
is 12.
Three x is 12
and divide by three.
We know our y coordinate now
is x equals four.
So that is my x coordinate.
Alright we're going
to do the same thing
to find the y intercept.
So to find the y intercept we
know that the x coordinate
of the ordered pair is zero.
Okay so if we take the
equation again,
the 3x minus 2y equals 12.
This time we're going
to let x equal zero
because you could see
up here I have zero for x,
I'm trying
to find the y coordinate
that goes along with that.
So I'm putting in zero
for x this time,
so we have three times zero
minus 2y equals 12.
So we have zero minus 2y
is 12.
Negative 2y is 12 and dividing
by two, negative two.
We have the y coordinate
of negative six.
So that would be my
y coordinate.
So now I have my x intercept
and my y intercept.
Now you might not need
to show all the steps I showed
over here on the left side.
For instance
when you let y equal zero
into 3x minus 2y equals 12,
you might notice
that if you plug
in that zero right in here
for y, this term negative 2y
will be zero.
So some people skip that
and they do
that in their head.
And just write 3x equals 12
and get the answer a little
bit quicker.
Same thing over here.
So when I'm going
to let x equal zero
into 3x minus 2y equals 12.
We're going
to do exactly the same thing.
When I plug in zero
for x you see this term 3x
will become zero.
So I can go directly
to negative 2y is 12
and we're dividing
by negative two I get y equals
negative six,
little bit faster.
In any case we have our x
intercept is four zero
and our y intercept is zero
negative six.
Let's do one more
quick example.
Let's find the intercepts
on the line 3x minus 5y
equals 10.
Alright so for the x intercept
we're going to put in zero
for y. So in this equation 3x
minus 5y equals 10,
we're going to put in zero
for y, which gives you 3x
equals 10 because this term
will pretty much
in essence disappear.
And so we have 10/3rds
when I plugged
in y equals zero right.
When I plugged
in y equals zero,
x was 10/3rds,
so that is the x coordinate.
And now for y intercept we
know we're putting zero
into the x coordinate
and so again we take the same
equation, but this time we're
going to put in zero
for the x coordinate right.
So this term disappears
and I have negative 5y
equals 10.
And so y is negative two
and that was
when I let x equal zero right.
So when x is zero,
y is negative two.
And you notice I did it the
faster method this way,
not showing plugging
in three times zero
and then simplifying it
to zero, et cetera.
Okay so if you're looking
for the x intercept,
the point is
to let y equals whoops,
don't know what
happened there.
Let y equal zero
and when you're trying
to find the y intercept you
let x equal zero.
In other words you put in zero
for x to find the y intercept,
you put in zero for y
to find the x intercept.