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This video is going to be about graphing lines from a table of values.
So if we have to do this, the first thing we might have to do if we're told to
graph a line from a table of values
is actually make the table of values.
Here's what's going on...
We might be given an equation like y equals 2x minus 1.
Well to make a table values from that equation
I'm going to draw two columns
the first column is going to be my x column the second column will be my
y column
and here
i'm going to put some numbers
let's start with a negative number, we'll use negative 1
and then maybe go up by 1,
so negative 1, 0, 1, 2
and now I'm gonna ask myself
when x is negative 1 in this equation
how much is y?
So let's see.
If x is negative 1, I've got 2 times negative 1, 2 times negative 1
is negative 2
and
negative 2 minus 1 would be negative 3
What happens when x is zero? Okay, so 2 times zero is zero
zero minus 1 is negative 1
I can keep going
When x is 1, 2 times 1 is 2 minus 1 is 1
when x is 2
2 times 2 is 4
and 4 minus 1
is 3
So now I've got a table of values, and now I have to graph a line from his table.
So let's make a graph,
draw my
x-axis
and my y-axis excess
put some tick marks in
2
3
And now what I want to do is plot some of these points.
What that means is this
I'm thinking of each pair numbers as a pair where x is the first number
and y is the second.
So I've got a situation where x is negative 1
and y is negative 3.
Now
to find where x is negative 1, I'm gonna look on my number line,
my x number line,
and that would be right here.
To find where y is negative 3 I'll look on my y number line,
that would be down here
and
i want to find
where both the x
where I've got both the x and the y. So I can think of it like this...
If I take this pen
and lay it where x is negative 1
and I take this pen and put it where y is negative 3,
where those pens cross
is going to be a place where x is negative 1
and y is negative 3.
So let's find that point... I could also just draw a dotted line
like this
instead of using the pens
and this point where the lines cross
is going to be
where x is negative 1
and y is negative 3. And I can label that point with an ordered pair
This is an ordered pair because they have to occur in order... the first number is
going to be the x number,
the second number is going to be the y number.
Okay I've got this point
I'm gonna erase these dots here 'cause they'll get in the way,
Let's take the point (1,1)
So I've got the point (1,1), that means I'm looking for a place where
x is 1, that would be over here,
and a place where y is 1,
that would be here.
So the place where those
two lines cross is going to be here.
That's going to be one comma one, that's my ordered pair.
Let's go to 2.
I want the x to be 2
and y will be 3.
I can just use my fingers and kind of estimate where that is. If I had graph paper
I'd know exactly where it was
and
that should be
right about here.
So there's my ordered pair,
2 comma 3
and I'll label that.
Now if I've done this neatly enough
I should be able to connect these three dots, this one this one and this one,
with a straight edge
and I should go through those points.
The reason for using three dots... I could just use two dots
but if I made a mistake with one of them I wouldn't know it. If I use three
and they all occur in a straight line
then I could be pretty sure that I'm right. I could also check
by looking at some other point. Here's another point I had...
0 and negative 1
and see is that line goes through that point.
So let's see. This is where
x is 0
it's over here
basically right on the y-axis
and this is where y is negative 1
and I do go through that point,
so this works.
Okay, and that's all there is to it.
Once again
you may given
an equation to begin with...
if you have the equation, you're going to then draw a table of values...
you're going to put some number into the table of values, usually you can put
pretty low numbers in the x column
and figure out
what you want in the y column, in other words
you take these numbers
plug them into the equation and see what y equals. That will give you pairs of
numbers,
you take those pairs
plot them on your graph, plots at least three of them,
connect them with a straight line and you can check by seeing if
any other pairs that you had
are also on that line.
And that's it,
take care for now, I'll see you next time.