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>> Hi, this is Julie Harland
and I'm your math gal.
Please visit my website
at yourmathgal.com,
where you could search for any
of my video's organized
by topic.
This is part five
of graphing linear
inequalities in two variables,
and on this video we're going
to graph these
two inequalities.
[Silence]
All right, before I do them,
put the video on pause and see
if you can do this one all
on your own;
3X minus 2Y is less than
or equal to 6.
All right, step one;
step one is always to graph it
as if it's an equation here,
right, so the line,
so we're going
to graph 3X minus 2Y equals 6
and we have
to decide whether we're going
to have a solid line
or a dotted line;
solid line means it's part
of the solution,
and so since it's got an equal
sign here, this is part
of the solution,
so use a solid line.
[Silence]
Since its part
of the solution.
[ Silence ]
All right,
now it's up to you how
to graph that.
I like using the X
and Y intercept method.
I think, well, if I put in 0
for X, what would Y be,
so when I put in 0 for X,
Y is going to be negative 3,
so 0 for X, Y negative 3,
I know that's going
to be one order pair
on this line,
and then I'm going to put in 0
for Y. If I put in 0 for Y,
I get 3X equals 6,
so X will be 2.
But, you can use any method
you want.
You can solve for Y and put it
in slope intercept form,
and so, if you did put this
in slope intercept form,
I'm just going
to remind you how to do
that quickly.
Negative 2Y is equal
to negative 3X plus 6
and divide by negative 2.
[Silence]
You would have Y equals 3
halves X minus 3,
and notice this tells you the
Y intercept is negative 3
and the slope is 3 halves,
I go over two and up three,
got the same two points,
and then we graph our line.
So, I'm using a solid line
because of the equation.
So, it doesn't matter the
method you use,
sorry my line doesn't look
very straight here,
I'm free drawing it,
but step one is
to simply graph that line
and use the solid line.
Now we have to decide
which side to shade;
all right,
so which side are we going
to shade?
Well, I pick a point off the
line and if I can,
I always chose 00.
So, I'm going to check 00.
[Silence]
And the original inequality,
and I'm only just going
to use the less than symbol,
because we're trying
to do that, that's supposed
to be a 2.
[Silence]
All right, so I'm going to put
in 2 for X and 2 for Y,
and hopefully you can see what
happens when I put in 2 for X
and 2 for Y,
I'm going to get 0 minus 0;
0 is less than 6,
and is that true?
So, that means 00 is
a solution.
[Silence]
A solution, just one of them,
so I'm going to shade
that side, where 00 is.
There we go.
Now, what if I had taken this
original equation,
3X minus 2Y is less than
or equal to 6 and tried
to solve for Y,
be careful here,
first you subtract 3X
from both sides;
I'm not sure that's all going
to show up here,
so I'll skootch it
over a little.
[ Silence ]
And, that guy didn't move it
over enough.
Here we go.
And then, when I divide
by negative 2,
be careful here, what happens
when you divide by a negative?
[Silence]
This is still less
than or equal.
When you divide by a negative,
that switches to greater than
or equal, so be careful.
[ Silence ]
So, I get Y is greater than
or equal to 3 halves minus 3,
and the reason I'm showing you
this is because notice,
if you have solved
for Y carefully,
you shade above the line,
because it says Y is greater
than or equal,
this is X. Okay,
but in any case,
it's always good
to check a solution anyway,
so you don't need to do this,
just sort of showing
that it all kind of matches
and makes sense if you do it.
[ Silence ]
All right,
let's go on to this problem;
X plus 3Y is less
than negative 3.
Try it on your own first,
put the video on pause,
get out some graph paper,
pay attention
to whether you need a solid
line or a dotted line,
check points, do your shading,
etc. All right,
what will our first step be?
Our first step will just
to be graph X plus 3Y equals
negative 3.
Now, remember,
it doesn't matter what method
you use to graph a line,
you just have
to get the correct line,
and am I going
to use a solid line
or a dotted line?
Is this part of the solution,
that line,
that's the big question.
No, it's not,
because there's no equal sign
up here, so we have
to use a dotted line,
since it's not part
of solution.
[ Silence ]
All right, so,
did you graph your line?
All right, I graphed my line,
and I know it's not really
straight, but I can't use a
ruler on my video
but you should use a ruler
or something
to make your dotted line look
straight on your paper.
So, here it is,
and you could have done this
by solving for Y
and putting it
in slope intercept form,
in fact, we could actually
take the original inequality
and easily solve
by subtracting X
from both sides.
I'm going to write
that as negative 1X minus 3,
and then dividing by 3.
Now, I'm dividing
by a positive number,
so remember, if I divide
by a positive number,
I don't have
to switch the inequality sign,
so Y is less than negative X,
I'm sorry,
negative one-third X minus
one, and that's the line I
have over here.
The slope intercept form gives
me the intercept of negative 1
and I have slope
with negative one-third,
but I actually did it
by using the X
and Y intercept method;
I plugged in 0 for Y to find
out X was negative 3,
which is right here,
and then I put it in 0 for X
to get Y was negative 1
right here.
In any case,
you hopefully have a
straighter line than me.
So the next thing is
to pick a point not
on the line, so I'm going
to chose 00,
because that's the easiest one
to plug in to the original,
and always plug it
in to the original, not this,
because you might have made a
mistake here,
so always plug it
into the original.
So, we're going to plug in 0
for X and 0 for Y,
which gives you 0 plus 0,
right, and is
that true or false?
Is 0 less than negative 3?
No, false, so that's not part
of solution, right?
[ Silence ]
So I do not want to shade
that part of the line.
I want, do not want
to shade the part of the line
where 00 is;
I want to shade the other side
of the line.
Now, if you'll look,
when we did solve,
I have Y is less
than negative one -third X
minus 1; remember
when you just Y on one side,
and you have less than,
it should be shaded below the
dotted line, so it matches
up there as well.
And there you have it.
In these 5 videos,
we've done a lot
of different inequalities;
graphing inequalities
with two variables,
so just keep practicing.
[ Silence ]
Please visit my website
at yourmathgal.com,
where you can view all
of my videos,
which are organized by topic.