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CCSS.Math: , ,

The following table
of values represents points x comma y on the
graph of a linear function. Determine the y-intercept
of this graph. So just as a reminder of
what the y-intercept even is, if you imagine a linear function
or a line if we're graphing it, if we imagine a
line, so let's say that is our line
right over there. This is our y-axis. This is our x-axis. The y-intercept is where
we intersect the y-axis. Now, what do we know
about the y-intercept? Well, at the y-intercept x
is going to be equal to 0. So this is the point
0 comma something. And so when people
are talking about, what is your y-intercept? They're usually
saying, well, what is the y-coordinate
when x equals 0. So we're really
trying to figure out, what is the y-coordinate
when x equals 0? So we know the x-coordinate
when y is equal to 0. So this is actually
the x-intercept. So this point right over
here is the point 2 comma 0. So when people say
x-intercept, that's the x-coordinate
when y equals 0. Well, they gave us
the x-intercept. So that right over there
is the x-intercept. But what's the y-intercept? What is the y-value
when x equals 0? Well, let's see. They give us what happens to
y when x is negative 2, when it's 1, when it's
2, when it's 4. So maybe we can backtrack
from one of these to get back to what happens
when x is equal to 0. So let me rewrite this table
so I can give ourselves a little bit more
breathing room. So let's say we have
x and we have y. x and y. And they already tell us that
when x is negative 2, y is 8. And I actually want
to think about what happens when x is
negative 1, when x is 0. Then they tell us
when x is 1, y is 2. When x is 2, y is 0. This right over here
is the x-intercept. When x is 4, y is negative 4. So they skip 2 right over
here. y is negative 4. So let's just see how y changes
with respect to changes in x. So when we go here, when x
changes by 1, y goes down by 2. And it's a line, so
it's going to have a constant rate of change
of y with respect to x. So similarly, when
x increases by 1, y is going to decrease by 2. So y is going to be 6 here. When x increases by 1 again,
y is going to decrease by 2. So we're going to get to 4. And we see it works. Because if we
increase by 1 again, then it is indeed the case
that y decreased by 2. And you see here when
we increase x by 2, then y decreases
at twice the rate. Because now we didn't
just increase by 1, we increased by 2. So now y is going
to decrease by 4. And what's constant
here is your change in y over your change in x. When x increases by
1, y decreases by 2. When x increases by
2, y decreases by 4. Either way you think
about it, your change in y for a unit
change in x is going to be equal to negative 2. But anyway, we actually
answered the question before without even
realizing it when we filled in all
of these values. What is the y-value
when x equals 0? Well, the y-value is 4. So the y-intercept here is 4. We didn't really
graph this to scale. It would actually look a
little bit more like this if we were to try to
graph it properly. So this right over here is 4. This right over here is 2. And our line looks
something like this. Our line will look
something like that.