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3.2, number 11.
Here we have another linear equation in two variables, and
we want to make a graph of it.
So let's start off by getting the x and y-intercepts.
So first, we'll put x as 0, and we'll find y.
Then we'll put y as 0, and we'll find x.
And then we'll just pick some other number for x.
And because I see some big numbers happening here, I'm
just going to pick a 1, and hopefully we won't get
anything too large.
All right.
So x is 0.
Let's get the y that goes with that.
So we put in x equals 0 into our equation.
We get 6 times 0 plus 5y equals negative 30.
That's the same as--
that's gone.
So the same as 5y equals minus 30.
Divide by 5 on both sides.
y equals minus 6.
So when x is 0, y is minus 6.
And that's our y-intercept.
Let's put in y equals 0.
6x plus 5 times 0 equals minus 30.
That guy is gone.
So we really have 6x equals negative 30.
Divide both sides by 6.
We get x equals minus 5.
So when y is 0, x is minus 5.
We have two ordered pairs, and to be safe, we always find a
third when we're graphing an equation.
And let's go ahead and put in x equals 1.
And you can pick whatever you want for x
or y, doesn't matter.
I just happened to pick 1.
6 times 1 plus 5y equals negative 30.
Well, that's the same as 6 plus 5y equals minus 30.
And now, we're just solving out the equation for y.
So I take away 6 on both sides.
That gives 5y equals negative 36.
And then I divide both sides by 5.
y equals negative 36 over 5.
Now, that doesn't work out to be an integer,
but that's all right.
That happens a lot when you're finding points
for a linear equation.
So we're going to go ahead and say 5 goes in 7 times to be
35, and there's a negative that we carry over and there's
1 left over.
So minus 7 and 1/5.
The other thing you can do if you prefer is take out your
trusty calculator.
36 over 5, 7.2.
So either way, fractions or decimals, that'll give us our
next point.
So minus 7.2 will be our third ordered pair up here.
When x is 1, y is minus 7.2.
And now we can graph our three points.
And when you're making your graph, what you want to be
careful of is it you make the scale so that all your points
are going to fit.
So our y-values have to reach down to minus 6 and minus 7,
so about minus 8-ish.
Our x-values have to go all the way to minus 5.
And then for the positives, they don't have to
go very far at all.
So we want to have a lot of negative space to make our
graph here.
Make every box equal to 1, but you could make every box equal
to 2, if you want.
It's just a matter of preference.
So we start with 0, minus 6 was our first point.
So we move 0 for x down 6 for y.
1, 2, 3, 4, 5, 6.
There's our first point.
Then minus 5, 0.
So we start at the origin.
Go negative 5 or left 5--
1, 2, 3, 4, 5-- for x.
0 for y means stay where we are vertically.
And then we have x is 1, over 1.
And then down 7.2.
1, 2, 3, 4, 5, 6, 7.
Somewhere around there.
And you break out the straight edge.
Put a line through it, arrows on both ends.
And there we have our graph of the equation.
