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# Graph from slope-intercept equation

Video transcript

We are asked to graph y is
equal to 1/3x minus 2. Now, whenever you see an
equation in this form, this is called slope-intercept form. And the general way of writing
it is y is equal to mx plus b, where m is the slope. And here in this case, m is
equal to 1/3-- so let me write that down-- m is equal to 1/3,
and b is the y-intercept. So in this case, b is
equal to negative 2. And you know that b is the
y-intercept, because we know that the y-intercept occurs
when x is equal to 0. So if x is equal to 0 in either
of these situations, this term just becomes 0 and
y will be equal to b. So that's what we mean by
b is the y-intercept. So whenever you look at an
equation in this form, it's actually fairly straightforward to graph this line. b is the y-intercept. In this case it is negative 2,
so that means that this line must intersect the y-axis at y
is equal to negative 2, so it's this point right here. Negative 1, negative 2, this
is the point 0, negative 2. If you don't believe me, there's
nothing magical about this, try evaluating or
try solving for y when x is equal to 0. When x is equal to 0, this term
cancels out and you're just left with y is equal
to negative 2. So that's the y-intercept
right there. Now, this 1/3 tells us the
slope of the line. How much do we change in
y for any change in x? So this tells us that
1/3, so that right there, is the slope. So it tells us that 1/3 is equal
to the change in y over the change in x. Or another way to think about
it, if x changes by 3, then y would change by 1. So let me graph that. So we know that this point is
on the graph, that's the y-intercept. The slope tells us that if x
changes by 3-- so let me go 3 three to the right, 1, 2, 3--
that y will change by 1. So this must also be a
point on the graph. And we could keep doing that. If x changes by 3,
y changes by 1. If x goes down by 3, y
will go down by 1. If x goes down by 6, y
will go down by 2. It's that same ratio, so
1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these
points are on the line, and the line is the graph of
this equation up here. So let me graph it. So it'll look something
like that. And you're done.