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.