00:01
So this is about using algebra and linear equations for simple modeling of a real -life scenario.
00:08
And the scenario in this case is we have the very famous leaning tower of pisa.
00:17
And so it's a tower that was built, you know, centuries ago.
00:23
And this is, you know, my drawing of a tower.
00:26
And the issue is, is that every year it keeps going.
00:30
This way.
00:31
It keeps tipping over.
00:33
And finally, it was just going to fall.
00:35
So some engineers decided, well, they will have to do something and bring it back up to the vertical.
00:47
But they didn't want to make it completely vertical.
00:50
They wanted to make it lean a little bit.
00:52
So the engineers, years, every time that they went to work, they were able to change the angle and make it more vertical.
01:09
So it's important when we're modeling to know what y and x represents in the scenario, in the real world scenario that we're modeling.
01:20
So y represents, the problem tells us, the number of millimeters that the tower was moved towards the vertical.
01:39
So this is y over here.
01:42
This is y, when they were moving the tower to make it vertical.
01:48
And then x represents days.
01:52
The engineers were working.
01:53
And this is quite typical to have x represent days, to have the x axis represent time.
02:01
It's very typical when we're modeling problems with algebra.
02:07
Okay, so we might as well make a note of this by giving names to our axes.
02:15
So this would be days, and this would be millimeters.
02:28
And you'll notice that i only drew the first quadrant because we're not going to have negative x values because we're not going to have negative time.
02:37
And we're not going to have negative y either because we're concerned with really the millimeters only going in one direction.
02:50
So this is the very simple equation, and the problem asks us to make a table of values using 0, 10, 20, and 60.
03:04
So let's make a table of values.
03:08
So x would go over here and y would go over here and then we want to make a table of values for 0, 10, 20.
03:18
The problem tells us these numbers and 60.
03:23
So, so one way to just do one way to show this is this is this is 1 .5x, right? and 1 .5x is the same thing as y, right? so what's 0 times 1 .5? what's 10 times 1 .5? well, we could say 10 times 3 over 2 because that's 1 .5.
04:01
So the 10 cancels and we're left with 15.
04:06
And then 20, same idea, 20 times 3 halves is equal to 30 and then 60 times three halves is equal to 60 it's equal to 90 so so the these are y values right so then y is 15 30 and 90 so that that part was easy and it wants us to write the information as order pairs so ordered pairs, it's basically how this information would appear if we were going to graph it.
04:58
So we have a point in our graph at 0 -0, and we have a point at 10 -15.
05:12
We have a point at 2030, and we have a point at 6090.
05:29
So now that we have these points, we might as well graph them, and we want to pick a scale for x and y that makes sense.
05:38
So we can see all these points and everything is to scale.
05:44
So let's see.
05:46
The x values are going up by 10, but we also have 60 over here.
05:54
So maybe we should maybe go up by 20...