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# Graphing using intercepts (old)

An old video of Sal where he draws the line y=3x-9 by finding its x- and y-intercetps. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Identify the x and
y-intercepts of the line y is equal to 3x minus 9. Then graph the line. So the x-intercept,
I'll just abbreviate it as x-int, that is where the
line intersects the x-axis. So where it
intersects the x-axis. Remember, this horizontal
axis is the x-axis. So when something
intersects the x-axis, what do we know
about its coordinate? Its x-value could be anything,
but we know it's y-value is 0. If we're intersecting,
if we're sitting on the x-axis
someplace, that means that we haven't moved
in the y-direction. That means that y is 0. So this means,
literally, that y is 0. So we need to find
the x-value defined by this relationship
when y is equal to 0. Similarly, when we talk
about the y-intercept, I'll do it down
here-- when we talk about the y-intercept,
what does that mean? Well, y-intercept
means-- so this is the y-axis right over
here running up and down. The y-intercept is
the point at which the line intercepts the y-axis. So what's going on? If we're at the
y-axis, our y-value could be anything depending on
where we intersect the y-axis. But we know that we haven't
moved to the right or the left. We know that our x-value
is 0 at the y-intercept. So over here, our
x-value is going to be 0. And to find the
actual point, we just have to find the
corresponding y-value defined by this relationship
or this equation. So let's do the first one first. The x-intercept is
when y is equal to 0. So we set y is equal to 0,
and then we'll solve for x. So we get 0 is
equal to 3x minus 9. We can add 9 to both
sides of this equation to isolate the x-term. So we get 9 is equal to 3x. These cancel out. We could divide both sides by 3. Divide both sides by 3. We get 3 is equal to
x or x is equal to 3. So the point y is equal to 0, x
is equal to 3 is on this line. And let me put it in order. x-coordinate always goes first. So it's 3 comma 0. So this is the origin. 1, 2, 3 is right over here. That is 3 comma 0. This right here is
the x-intercept. And remember, notice that
point lies on the x-axis, but the y-value is 0. We haven't moved up or down. When you think
x-intercept, you say, OK, that means my y-value is 0. So I have to solve
for the x-value. Now we do the opposite
for the y-intercept. And the y-intercept, we're
sitting on this line, x-value must be 0. So let's figure out what y is
equal to when x is equal to 0. So y is equal to-- I want
to do it in that pink color. y is equal to-- y is equal
to 3 times-- x is 0 now. 3 times 0 minus 9. Well, 3 times 0 is just 0. So 0 minus 9. Well that's, just
equal to negative 9. So we have the point
0 comma negative 9. So when x is 0, we
go down 9 for y. 1, 2, 3, 4, 5, 6, 7, 8, 9. So right there is the
point 0 comma negative 9. Notice, it sits on the y-axis. That's why it's the y-intercept. And the x-value is 0. We haven't moved to
the left or right. All you need is two
points for a line, so we're now ready to graph. We essentially just have
to connect the dots. So it's going to look
something like this. It's going to look
something-- our line. I don't have a good
line tool, so I'm going to try my best
to draw it nicely-- is going to look
something like that. And you just keep going. You just keep going. You want to do a straight line. So it just keeps going on
and on and on like that. It just keeps going. And I could keep going all
the way in that direction, and then-- but then my line
doesn't look as straight all of a sudden. I think you get
the general idea. I can keep going like that,
and then keep going like that. I don't have a nice
ruler to do it with. And we're done.