>> 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 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 a line
if we know the equation
of the line.
Alright so let's find the
intercepts
on the line 69x minus 12y
equals negative 46.
Alright well if we're trying
to find the x intercept,
keep in mind we know
that for the x intercept,
it's in the form something
zero so y must be zero.
So we already know what the y
coordinate is.
And for the y intercept we
know the x coordinate has
to be zero.
Okay so let's do the x
intercept first.
So if we look at the line,
equation of the line 69x minus
12y equals negative 46,
we're trying to finish filling
out this order pair
and it says to plug in zero
for y. So if we put in zero
for y, that term negative 12y
will end up being zero
and I will get 69x equals
negative 46.
So we'll just divide both
sides by 69 and reduce it.
Let's see 23 goes into both
of those, so that's negative
2/3rds, so you might not
realize that reduces.
But keep in mind 46,
so that's a negative two times
23 and 69 is three times 23.
If you're not sure
if something reduces,
just factor it
and then you can cancel the
common factors.
So when I plugged in zero
for y I got negative 2/3rds,
so the x coordinate
of the x intercept is
negative 2/3rds.
So the x intercept is negative
2/3rds zero,
there's our x intercept.
Alright why don't you try
doing the y intercept,
putting the video on pause
and then turning it on again.
Alright we're going
to do the y intercept
same way.
So if we have our equation
of the line 69x minus 12y
equals negative 46
and now we're plugging in zero
for the x coordinate right.
That will give us 69
times zero.
That zero,
so this term basically
disappears
and we have negative 12y
equals negative 46.
Now we'll just divide both
sides by negative 12
and again we're going to have
to reduce.
So a negative divided
by a negative will be
positive, so let's see.
What goes into both 46 and 12?
Well two goes
into both of them.
So if I divide the top by two,
46 divided by two is 23
and 12 divided by two is six.
So it looks
like our y coordinate is going
to be 23/6ths.
It's reduced,
so we've got our x coordinate
and we've got our y
coordinate, y intercept,
which is zero 23/6.