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CCSS.Math:

Find the slope of the line
pictured on the graph. So the slope of a line is
defined to be rise over run. Or you could also view it as
change in y over change in x. And let me show you
what that means. So let's start at some
arbitrary point on this line, and they highlight
some of these points. So let's start at one of
these points right over here. So if we wanted to start one
of these points-- and let's say we want to change our x
in the positive direction. So we want to go to the right. So let's say we want
to go from this point to this point over here. How much do we
have to move in x? So if we want to move in x,
we have to go from this point to this point. We're going from
negative 3 to 0. So our change in x-- and
this triangle, that's delta. That means "change in." Our change in x is equal to 3. So what was our change in y when
our change in x is equal to 3? Well, when we moved from
this point to this point, our x-value changed by 3, but
what happened to our y-value? Well, our y-value went down. It went from positive
3 to positive 2. Our y-value went down by 1. So our change in y is
equal to negative 1. So we rose negative 1. We actually went down. So our rise is
negative 1 when our run-- when our
change in x-- is 3. So change in y over change
in x is negative 1 over 3, or we could say that our
slope is negative 1/3. Let me scroll over a little bit. It is negative 1/3. And I want to show you that we
can do this with any two points on the line. We could even go further
than 3 in the x-direction. So let's go the other way. Let's start at this
point right over here and then move backwards
to this point over here, just to show you that we'll
still get the same result. So to go from this point to that
point, what is our change in x? So our change in x is
this right over here. Our change in x is that
distance right over there. We started at 3, and
we went to negative 3. We went back 6. Over here, our change in
x is equal to negative 6. We're starting at
this point now. So over here our change
in x is negative 6. And then when our change
in x is negative 6, when we start at this
point and we move 6 back, what is our change
of y to get to that point? Well, our y-value went from 1. That was our y-value
at this point. And then when we go back to
this point, our y-value is 3. So what did we do? We moved up by 2. Our change in y is equal to 2. Slope is change in y over
change in x, or rise over run. Change in y is just rise. Change in x is
just run, how much you're moving in the
horizontal direction. So rise over run in this
example right over here is going to be 2
over negative 6, which is the same
thing as negative 1/3. And you could verify
it for yourself. Take any of these
two points, start at one of these two
points, and figure out what is the run to
get to the next point, and then what is the rise
to get the next point. And for any line, the
slope won't change. Let me do it again. Over here, we had to move in the
positive 3 direction, so that is our run. So this right here
is positive 3. That's our run. But what's our rise? Well, we actually went down,
so we have a negative rise. Our rise is negative 1. So we have negative
1 as our rise. We went down. And our run was positive 3. So our slope here
is negative 1/3.