00:00Friends, today we're going to talk about different types of proportions.
00:03The first type of proportion we have is direct proportion.
00:06What is direct proportionality?
00:07If, when one of two quantities increases, the other also increases at the same rate.
00:32Or if one decreases while the other decreases at the same rate.
00:54These two quantities are directly proportional, or simply said to be proportional.
01:18So, friends, if one quantity increases while the other increases, or if one decreases while the other decreases proportionally, we say these two quantities are directly proportional.
01:27The ratio of two directly proportional quantities is constant, folks.
01:46Let's take y and x as examples, for instance.
01:49If y and x are directly proportional
01:59We will say that
02:00y divided by x equals k, the constant of proportionality.
02:05or
02:06y equals k times x, which is a proportionality ratio.
02:12It is said that y equals k times x.
02:17Friends, the graph of y equals k times x.
02:26Of course, before moving on to the graph, I also need to know this.
02:30In order to determine our graph as well...
02:31Let's consider x and y.
02:35For example, if x goes like this: 1, 2, 3, etc.
02:41Let's consider Y.
02:43What needs to happen for this ratio to change, guys?
02:48K
02:48I'm at an easy point with the ratio 2, 3.
03:00Let's consider y.
03:07Well, there's a Barbara!
03:09As you can see, our plane is here, folks, it's not equal to zero, this isn't included, this is zero.
03:16What happens if our point is zero? Friends, this won't work, there won't be abundance, and at the same time, it will be zero.
03:22There would be an uncertainty level of divided by zero, which is impossible, therefore we have a graph like this.
03:27Let's do that and immediately place our numbers in their places: one, two, three, one, what does that go to?
03:39Friends, in y, k is 2 times k, and here it's 3 times k, as you can see, of course.
03:52As I said, our k must be greater than zero, so our y is equal to k multiplied by both of us, and this is what we put on the graph.
04:01Having said that, I'd like to add a few notes: the numbers x, y, and z are in order.
04:16with the numbers abc
04:25proportional
04:27that is, if it is directly proportional
04:34How do we write, friends? Another task...
04:37x divided by a equals y divided by b, which equals z divided by c
04:42In the shape of y, which is equal to k, our proportion letter would also be k. Another final note, friends.
04:50a and b are non-zero.
05:01Let r be the numbers.
05:08What will happen, friends, that satisfies the equation y equals a times x plus b?
05:25x and y values
05:34They are not directly proportional, friends.
05:36Let's pay attention.
05:45but let's say
05:48The amount of change in x
05:59the amount of change of y
06:11proportional
06:11proportional
06:12Friends
06:12astonishment
06:14proportional
06:15proportional
06:16proportional
06:17proportional
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