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CCSS Math: 8.F.B.4, HSF.LE.A.2

Find the slope of the
line in the graph. And just as a bit of a review,
slope is just telling us how steep a line is. And the best way to view it,
slope is equal to change in y over change in x. And for a line, this will
always be constant. And sometimes you might see it
written like this: you might see this triangle, that's a
capital delta, that means change in, change in
y over change in x. That's just a fancy way
of saying change in y over change in x. So let's see what this change
in y is for any change in x. So let's start at some point
that seems pretty reasonable to read from this table right
here, from this graph. So let's see, we're starting
here-- let me do it in a more vibrant color-- so let's
say we start at that point right there. And we want to go to another
point that's pretty straightforward to read,
so we can move to that point right there. We could literally pick any
two points on this line. I'm just picking ones that are
nice integer coordinates, so it's easy to read. So what is the change in y and
what is the change in x? So first let's look at
the change in x. So if we go from there
to there, what is the change in x? My change in x is
equal to what? Well, I can just count it out. I went 1 steps, 2
steps, 3 steps. My change in x is 3. And you could even see
it from the x values. If I go from negative 3
to 0, I went up by 3. So my change in x is 3. So let me write this, change in
x, delta x is equal to 3. And what's my change in y? Well, my change in y, I'm going
from negative 3 up to negative 1, or you could
just say 1, 2. So my change in y, is
equal to positive 2. So let me write that down. Change in y is equal to 2. So what is my change in
y for a change in x? Well, when my change in x was
3, my change in y is 2. So this is my slope. And one thing I want to do, I
want to show you that I could have really picked any
two points here. Let's say I didn't pick-- let me
clear this out-- let's say I didn't pick those two points,
let me pick some other points, and I'll even go in
a different direction. I want to show you that you're
going to get the same answer. Let's say I've used this as my
starting point, and I want to go all the way over there. Well, let's think about the
change in y first. So the change in y, I'm going down
by how many units? 1, 2, 3, 4 units, so my change
in y, in this example, is negative 4. I went from 1 to negative
3, that's negative 4. That's my change in y. Change in y is equal
to negative 4. Now what is my change in x? Well I'm going from this point,
or from this x value, all the way-- let me do that in
a different color-- all the way back like this. So I'm going to the left, so
it's going to be a negative change in x, and I went 1,
2, 3, 4, 5, 6 units back. So my change in x is equal
to negative 6. And you can even see I started
it at x is equal to 3, and I went all the way to x is
equal to negative 3. That's a change of negative 6. I went 6 to the left, or
a change of negative 6. So what is my change in
y over change in x? My change in y over change in x
is equal to negative 4 over negative 6. The negatives cancel out
and what's 4 over 6? Well, that's just 2 over 3. So it's the same value, you just
have to be consistent. If this is my start point,
I went down 4, and then I went back 6. Negative 4 over negative 6. If I viewed this as my starting
point, I could say that I went up 4, so it would
be a change in y would be 4, and then my change
in x would be 6. And either way, once again,
change in y over change in x is going to be 4 over 6, 2/3. So no matter which point you
choose, as long as you kind of think about it in a consistent
way, you're going to get the same value for slope.