00:01
Let's find the area between these two graphs.
00:03
Well, the first thing we need to know is the area that it's bounded by.
00:06
So i'm going to come over here and say x equals 15 minus 4y, and then i'm going to substitute that for x here.
00:13
So 15 minus 4y plus 6 equals y squared.
00:18
21 minus 4 y is y squared, and i want to set that equal to 0 and say y squared plus 4 y minus 21 equals to 0.
00:29
So i factor this.
00:30
I get y plus 7, y minus 3, we'll get y equals negative 7, y equals 3.
00:38
So we need to know the x values that go along with this.
00:41
So i'm going to put negative 7 and i'm going to put 3 into my ordered pairs.
00:47
And then i'm going to substitute that in for y and get my x values.
00:51
So when i substitute 3 in there, i'm going to get 12 minus 15 minus 12, which is 3.
00:57
When i put negative 7, i'm going to get 15 plus plus 28, which is going to be 30, 43.
01:04
So we're looking at the ordered pairs, 43, negative 7, and 3 -3, that we want to find the area between.
01:15
Well, when looking at this, i'd just see that some of the graph is going to be above the x -axis, and some is going to be below.
01:21
The reason i know that is because we have this negative 7 is negative, and the y values are opposite of values.
01:28
So somewhere in between here, our graph is going to come.
01:31
Cross that x -axis.
01:34
So we need to figure out what that is going to be.
01:37
Where does it, where do we have our graphs, graph's region go from the positive side of the x -axis to the negative side? so to find that x intercept, we're going to let y equal zero.
01:51
If i let y equal zero here, then i'm going to have x plus zero equals 15, so x would equal 15.
02:00
If i let y equal zero here, if i let y equal zero here, they're going to have x plus 6 equals 0, x equals negative 6.
02:07
Well, this is outside our region, so we don't want to deal with that.
02:10
So we know what i have the number 15.
02:12
So here at 15 is where it's going to cross that x -axis.
02:17
So that means we have a positive region from 3 to 15, and then we have a negative region from 15 to 43...