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## Lesson 9: Slopes don't have to be positive

Current time:0:00Total duration:6:33

# Intro to intercepts

CCSS Math: 8.F.A.1, HSA.REI.D.10, HSF.IF.C.7, HSF.IF.C.7a

## Video transcript

- [Voiceover] Let's say that
we have the linear equation, y = 1/2x - 3. So if we wanted to draw
the line that represents the set of all points, all the
coordinates where the x value and the y value satisfy this equation, we could start off by just trying to draw, by trying to draw a few of those points, and then connecting them with a line. Let's set up a little table here x, y. And we can just try a
couple of x values here, then figure out what the
corresponding y values are. I'm going to pick x
values where it's going to be fairly easy to
calculate the y values. Let's say when x is equal to zero, then you're gonna have 1/2 x 0 - 3, well then y is going to be -3. When x is, let me try x
= 2, because then 1/2 x 2 is just gonna be 1. So when x = 2, you're going to have 1/2 x 2 = 1, -3 is -2. When x is equal to, let's try 4. So 1/2 x 4 is 2, and then -3 is -1, and we could keep going but actually all we need is two points for a line. So we're ready to plot
this line if we'd like. The point 0, -3 is on this line. 0, -3 and actually let me do
this in a slightly darker color so that we can see it on
this white background. 0, -3 is on the line,
2, -2 is on the line. So 2, -2 and then we have 4, -1. So when x is 4, y is -1, and I could draw a line
that connects all of these so it would look something like... If I, let's see if I could do this. It would look something like, it would something like, like that. So this right over
here, this is literally, this is the graph of y = 1/2x - 3. Now when we look at a graph like this an interesting thing that
we might want to ask ourself is where does the graph
intersect our axes? So first we can say, well where does in intersect our x-axis? When you look at this, it looks like it happens at this point right over here. This point where a
graph intersects an axes this is called an intercept. This one in particular is
called the x-intercept. Why is it called the x-intercept? Because that's where the graph is intersecting the x-axis and the x-intercept, it looks like this is at the .6, 0. Now it's very interesting, the x-intercept happens when y = 0. Remember, you're on the x-axis when you haven't moved up
or down from that axis which means y = 0. So your x-intercept
happens at x = 6, y = 0. It's this coordinate. Now what about the y-intercept? Well the y-intercept is
this point right over here. This is where you intersect or I guess you could say intercept the y-axis. So this right over here, that over there is the y-intercept. The y-intercept is at the coordinate that has a 0 for the x-coordinate. X is 0 here and y is -3. X is 0 and y is -3. This was actually one of the points, or one of the pairs
that we first tried out. You can validate that 6,
0 satisfies this equation right over here. If x is 6, 1/2 x 6 is 3,
-3 is indeed equal to 0. So now that we know
what an x-intercept is, it's the point where a
graph intersects the x-axis or intercepts the x-axis
and the y-intercept is the point where a graph
intercepts the y-axis or intersects the y-axis. Let's try to see if we can
find the x and y-intercepts for a few other linear equations. So let's say that I had
the linear equation. Let's say that I have 5x + 6y = 30. I encourage you to pause this video, and figure out what are
the x and y-intercepts for the graph that
represents the solutions, all the xy pairs that
satisfy this equation. Well the easiest thing to do here, let's see what the y value is when x = 0 and what x value is when y = 0. When x = 0 this becomes 6y = 30. So 6 times what is 30? Well y would be equal to 5 here. So when x is 0, y is 5. What about when y is 0? Well when y is 0, that's going to be 0, and you have 5x = 30. Well then x would be equal to 6. Then x would be equal to 6. So we could plot those points, 0, 5. When x is 0, y is 5. When x is 6, y is 0. So those are both points on this graph and then the actual graph is going to, or the actual line that
represents the x and y pairs that satisfy this equation
is going to look like, it's going to look like this. I'll just try. So I can make it go, it's
going to look like... It's going to go through those two points. So it going to...I can make
it go the other way too. Let me see. It's going to go through those two points and so it's going to
look something like that. Now what are its' x and y-intercepts? Well, we already kind of figured it out but the intercepts themselves, these are the points on the graph where they intersect the axes. So this right over here,
this is the y-intercept. That point is the y-intercept and it happens, it's
always going to happen when x = 0, and when x
= 0 we know that y = 5. It's that point, the point 0, 5. And what is the y inter...what
is the x-intercept? The x-intercept is the
point, it's actually the same x-intercept for this
equation right over here. It's the point 6, 0. That
point right over there.