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>> In this video, we'll go over how to graph a line
if you know a point on the line and its slope.
For example, graph the line that passes
through the point negative 3, negative 4,
and has a slope of 3 halves.
Well, we know 1 point on the line, negative 3, negative 4,
so we can start with that.
So we can add a piece of graph paper and we're going
to plot the point negative 3, negative 4,
so here's the center, the origin, you go negative 3,
negative 4, and we have 1 point on the line.
Now, we're going to use the idea of slope and rise over run
to find another point.
So, we know that the slope is rise over run, so the trick is
to write the slope as a fraction,
which actually it is written, it's 3 halves, right?
So we've written it as a fraction, and now we want
to put signs in for the numerator and denominator
so that it stays positive 3 halves.
So we can think of that as plus 3 over plus 2, therefore,
figuring out if we do a run of positive 2 and rise
of positive 3, we should find another point on the line.
Alright, so we have to start from our starting point,
which is negative 3, negative 4, and we need to go a run
of what's in the denominator?
Positive 2, 2 to the right, and then a rise
of positive 3, which is up 3.
And there's another point on the line.
Now you could just do this again from this new point,
you'd do a run of positive 2 and you go up 3
and I have another point on the line.
And this is a nice thing to do, what's cool about slope,
if you don't have a straight edge with you it's easier
to connect the dots when they're close together.
And so I can keep going until I run out of space.
Now the question is how can I get a point to the left?
Keep in mind that you could also write the slope,
as long as it reduces to 3 halves, we're ok.
So, we could multiply the top and bottom by a negative 1
and then that would be negative 3 over negative 2.
If you want to think about it that way, watch what happens
from my starting point negative 3, negative 4.
I can do a run of negative 2, which means 2 to the left,
and then go down 3, because the rise is negative 3,
which means it goes down and there we have it.
So there's always going to be
at least 2 ways you can write the slope.
If you have a minus in front of the fraction part,
that's not as helpful, you want to put it either
in the numerator or the denominator.
So now I graph by my line by connecting the dots.
[ Silence ]
>> So I've drawn the line and then the question is does
that pass through the point negative 3, negative 4?
And does it look to you like it has a slope
of positive 3 halves?
Yes. Let's do another one.
One more quick note about this.
You could have written this as 6 over 4,
you could write any fraction that reduces to 3 halves,
and if you start from this first point, negative 3, negative 4
and do the rise over run of any fraction, you will still end
up with the point on the line.
So, for instance, another way to write 3 halves, multiply the top
and bottom by 3 for instance, would be 9 6ths.
And if I started here at the bottom, if went over 6 and up 9,
I do get this point on the graph as well.
You could also go over 2 inches and 3 inches.
You just have to go over whatever unit you want,
it's easier if you use graph paper,
use the units on the graph.
But, you could go over 2 feet and up 3 feet,
and you would also get a point of -- point on that line.
So here's another one.
Graph the line that passes through 2 negative 4,
and has slope of negative 3 5ths.
Okay, so always the first thing we're going
to do is plot the point we know that's on the line.
So we're going to plot 2 negative 4.
So here's X, here's Y, and starting
from the origin we're going to go over 2, negative 4.
Next, we want to write the slope as a fraction.
Now it's written as negative 3 5ths, what I mean is to write it
as a fraction without the minus sign out in front like that.
So notice it's negative, so that means either the numerator
or the denominator needs to be a negative number,
and the other needs to be a positive.
So I could write this as negative 3 over positive 5.
So remember we've got the rise over the run.
Alright, so let's say we use that.
So from my point, 2 negative 4, I'm going to run 5, positive 5,
so I'm going to go the right, 1, 2, 3, 4,
5 and I'm going to go down 3.
Now if I do it again, I'm going to be -- you know --
way off my graph paper that I've drawn here.
So that's why it's nice to know,
and by the way right here you can go ahead and draw the line,
but let's say wanted to get a few more points,
or at least 1 more point, I could of written it
as positive 3 over negative 5.
That will also work because that also reduces to negative 3 5ths.
And if I use this instead, I'll get some points
to the left of my ordered pair.
And in fact, anytime the denominator's negative you'll
get ordered pairs to the left.
And when the denominator's positive obviously you're going
to find some points to the right.
So, starting from my point, 2 negative 4, if I'd written it
as positive 3 over negative 5, I would go to the left 5 spaces
and then I would go up 3, and that would be right here.
Think, 1, 2, 3, 4, 5, up 3 and I can do that again.
From this point, I can go to the left 5, 1, 2, 3, 4, 5, up 3,
and now I have a lot of points, a little bit easier to go ahead
and draw the line through those points.
Now, does that look like, if I'd drew a line
that if got a slope of negative 3 5ths?
It is slanting in the direction that has negative slope.
And it is going through the point 2 negative 4.
So the last thing is simply to draw the --
get out something straight --
be careful, and draw a straight line as best you can.
And so there's the line.
Alright, here's one more.
Graph the line that passes through 2 negative 1,
and has a slope of negative 3.
So we're first going to plot 2 negative 1, always take 1 point,
the point you know it goes through
and at least get that on your graph.
So, I've got 2 negative 1.
And then starting from that point we want
to find another point by using this slope.
So I need to write the slope as a fraction.
Alright, so how are we going to write negative 3 as a fraction?
Well, we can write negative 3 over positive 1.
Or we can write positive 3 over negative 1.
Or we could write it a whole bunch of other ways,
for instance, negative 6 over positive 2,
or something like that.
So, we have to choose one of these to find some more points.
So, so, we're going to start at the point
and let's choose this first slope,
negative 3 over positive 1.
So I'm going to go and run positive 1, 1 to the right,
and down 3, and I've got another point, and do it again,
over 1 to the right, and down 3.
And of course that's all I can get,
I'm getting it off my graph, right?
So how about instead we use the positive 3 over negative 1
for my starting point of 2 negative 1.
That would be my run is negative 1, that means go
to the left 1 and up 3.
And the left 1 and up 3, and you can see I can get a lot more
points by using that slope.
Now a common mistake is to use the slope starting
from the origin and make sure you don't do that.
You've got to start from the point that's on the line
for sure, which in this case is 2 negative 1.
So, my last step here would be to connect the dots.
So, here's the line, alright?
So, reviewing the steps are to plot the point, write the slope
as a fraction, and use the idea of rise over run
to find more points on the line.