hi guys it's me teacher going in today's video we will talk about direct variation and for this kind of topic this one is the second quarter for grade 10 students here in the Philippines and the creation that are that is being used in representing direct variation is simply Y is equal to KX now when you say variation that is y varies directly as X if Y is expressed as the product of some constant number K and X in this given equation guys the two variables here are y and x and this variable K is the constant of variation meaning this one is a number K represents a number and considered as the constant of variation now simple definition or simple things about direct variation direct variation if one quantity increases on the other hand if one quantity decreases in 90 degrees meaning in case if you miss a it goes up sir what about the other one variable or is some quantity the other variable will also decrease variation so right now we have here uh two different examples of direct variation so um the other value will also increase so look at this given table of values we have your dividable X in dividable way we're in the values of X are 2 4 and 16. and as you can see the behavior of these numbers or these quantities is going up or increasing while here in the variable y we have 4 8 and 32 as the value of X increases and tendency increase the new value non-variable y that's why this table of values represents direct valuation another thing what we have here is a given graph ICS variation characteristics and direct variation is that it represents a straight line second origin or Center in X and Y axis as the value of X increases the value of y also increases okay definitely this one is an example of direct variation so I want to show you another formula if this is a general formula for direct variation Y is equal to KX is getting the constant of variation the question of variation can be solved in manipulating this kind of equation what you need to do is divide both sides of the of the equation by X and as you can see we can cancel this out and what we have now is key is equal to y over X meaning to say that this one is the formula for the constant of variation when it comes to direct variation so let's have here a problem that would give you the idea May encounter a new possible questions to the recommodation so we have here y varies directly as X if Y is equal to 12 and X is equal to 4. here's the problem find the constant of variation what is the equation of variation and what is x when y is 36. so right now first thing we need to do is to find the constant of variation knowing that this one is a direct variation we need to translate this first y varies directly as X statement that is simply equal to y is equal to k x it is no general formula nothing y varies directly as X now somebody to find the constant of variation how are you going to answer letter e the answer letter e if Y is equal to 12 when X is equal to 4. so melon time value num X I know Y is which is equal to 12. nothing is equal to 4. so simple you can you can directly use this formula and manipulate the equation or gametrated on K is equal to Y over X okay so we have k is equal to y over X again this variable K is the constant of radiation to find the constant substitute the value of y which is 12. that is 12 over your X which is 4. so to simplify this your K is equal to 12 divided by 4 which is equal to 3 meaning this is the constant of variation so we are done answering letter A now let's move on to letter b sir what is the equation no for decrease when since we are done finding out the value of K to answer letter b what you need to do is to use this y is equal to your k x your K is equal to 3 meaning substitutely as k then X this is now decrease or another variation Y is equal to 3x again no further solution using the general equation again using the general equation y your case three and then X that's it so let's move on with letter c for letter c what is x when Y is equal to 36 million Behavior um from Y is equal to 12 dito Y is equal to 36. from 12 to 36 a movement and numbers nothing is increasing okay meaning if we are expecting for the value of x if this is 4 so let's continue um to answer this Y is equal to 3x okay because [Music] so what is x when Y is equal to 36 so Y is equal to 36.36 so this is 36 is equal to 3x three please we replace the variable y I started by 36. International and to find the value of x what is X divide both its battery cancel cancel your X is equal to 36 divided by 3. and that is equal to 12. and this is the answer for letter C check nothing from Y is equal to 12 again 36 increasing from X which is 4 it became 12. so another increase in value so I hope you guys to learn something from this video for a form this example and let's set the second example guys for the second example what we have here is a given table of values okay table of values same question we will try to find the constant of variation so constant of variation foreign for letter e Y is equal sorry Y is equal to KX and for the formula of constant of variation that is K is equal to y over X your K is equal to Y so 6 over X which is 3. what is the answer guys the answer is 2. K is equal to Y which is 10. over your X which is 5 10 divided by 5 is equal to 2. so by resting guys 14 divided by seven it will also give you two meaning the horizontal variation is simply two okay so let's move on with the letter B for letter b this is your general formula copy the variable y your constant is 2 or case two so equals to two accidents mean okay so what about letter C what is y when X is equal to nine so potassium I think y is so [Music] um see using this formula Y is equal to 2x again your X is equal to 9 . that is y is equal to times multiply Y is equal to 2 times 9 which is 18. so 27. as simple as that for open signal X seven again nine the opportunity is greater than 14 and that's it 18 is greater than 14. so as I hope you learned something from this video guys on how to find um the constant of variation the creation and the missing value of a given problem so if you're new to my channel don't forget to like And subscribe button for you to be updated certain latest uploads again it's miniature gone bye