00:01
This problem gives us the enrollment in public colleges for a few select years, those years being 2006 and 2012.
00:12
And it asks us to estimate using a linear approximation, assuming a linear relationship.
00:19
So we're assuming a linear relationship here, and we need to predict what those values may be in 2003 and 2009.
00:27
Now perfectly, right in between 2000 and 2006, you have 2003.
00:34
And the same thing immediately in between 2006 and 2012.
00:38
You have 2009.
00:39
So therefore, we can use our midpoint formula to estimate this here.
00:44
So in doing this, we'll start with a 2003 example, our part a for this problem.
00:49
So we start with m equals and then our x1 plus x2, which will be 2000 plus, plus.
00:59
2006 and that's divided by two and then our y1 plus y2 our y1 here would be 11 ,753 plus 13 ,180 and that is also divided by two and very similarly actually i should start off by first noting that this is all in thousands of students here so it's all in thousands of students.
01:29
So now in calculating this out, we have 2000 plus 2006 divided by two.
01:35
That's bringing us 2003, which is the year that we want.
01:39
And then our y values, adding them together and dividing by two...