Intercepts from a table

0:00The 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.

0:20This 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?

0:41They'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.

1:00So 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.

1:21So 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.

1:44And 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.

2:03So 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.

2:28So 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.

2:51Because 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.

3:20But 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.

3:41So 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.