[Music] hello mark awamat in this video lesson we will discuss about direct variation our objectives illustrate situations that involve direct variation translate into variation statement a relationship involving direct variation between two quantities given by a table of values a mathematical equation a graph and vice versa and solve problems involving direct variation remember there is a direct variation whenever a situation produces pairs of numbers in which the ratio is constant this can be expressed into mathematical statement or equation as y is equal to kx where k is equal to y over x is the constant of variation or constant of proportionality this statement can be y values directly as x y is directly proportional to x and y is proportional to x statement into equation okay depend is a variable in a gaga meeting so y is equal to y and x organic to the apache nano then translate and also this statement mean that for two quantities x and y and increase in x causes an incr increase in y as well similarly a decrease in x causes a decrease in y okay let's have first an application of the relationship between the distance or the time travel and the distance okay this is application of a direct variation using his bicycle kyle travels a distance of 10 kilometers per hour on a steep road so first okay given the table of values so in one r he traveled 10 kilometers in two hours he traveled 20 kilometers in three hours he traveled 30 kilometers in four hours he traveled 40 kilometers and in fifth okay after five hours he traveled ready 50 kilometers so let's try to answer the following question show that the distance the vars directly as time t draw the graph of d against t write an equation showing the relationship between d and t how far kyle traveled after eight hours and ten and a half hours okay let's answer first letter a show the distance d virus directly as time so nothing nothing generation okay so nothing generation about what it says so if they divide language and d over t so sao na if this 10 and times 1 so 10 divide 1 the answer is 10. so and so pangala that is 20 divide two so the answer is still ten at sapangatlo thirty divide three so still the answer is ten and then up at forty divide four the answer is ten and last fifty divide 5 the answer is 10 so therefore uh 10 is constant so it makes a b hand divides directly as t okay so again and constant nothing theta is 10. next draw the graph of d against t okay so using the cartesian plane you can plot the ordered pairs of the given point so and then this now so that is 110 say three on next is 220 330 440 and 550 so notice that is the time increases so when the time is increases the distance also increases as the time decreases the distance decreases in fact as a time our number of hours is double the distance trouble also doubled so that is the uh relationship of the direct variation and write an equation showing this relationship between d and t so not in an equation which is 10 divided valuation yen so on a b sub none so that is since then generation nila so the equation relating the nt is d is equal to 10 times t so try not in check is 3 so 10 times 3 so the distance is 30 correct so and letter d so eb sabine equation that indeed is d is equal to 10 t or 10 times t so say letter d how far kyle traveled after eight hours and ten and a half hours so using our equation so when p is equal to eight so substitute like not n so ten times eight the answer is 80 so 80 kilometers after eight hours now another 10 in 10 and a half hours 10 and one half now so gangnam lang dance up to chicago so that is 10 times one half okay so ten times one half and ten times ten and a half that is one hundred five so it makes a big head after ten and one half kilometer 10 and one half hours so he traveled already 105 kilometers okay so again this is an application of direct variation showing the relationship between the distance and the time trouble okay for example number two write an equation for the following statement so pano banated it translate no among a statement into an equation so first the failure of a passenger varies directly as the distance d of his destination by the way class variables since my word time bar is directly detailed so that is uh for direct variation so panel nothing it translates into a equation so that is f is equal to k d so lagging my k can say okay that is our constant where k is f over d so that and nothing so soon again next the weight w of an object is directly proportional to its mass m so again if i got directly directly proportional so pares for direct variation so palu natin going equation so it translates into equation so that is w is equal to k m so where k is equal to w over m and for letter c the area a of a triangle is proportional to its height h so that is a is equal to k h where k is equal to a over h so again nothing it translates into equation numeral statement okay so let's apply no you need to tune in that indeed is example number two for example number three if y varies directly as x so then general if y varies directly as x and y is equal to 24 when x is six find the variation constant constants and the equation of variation so panel nothing gagawin so first scale and that is translation statement that the y varies directly as x so that is y is equal to k x equation of variations in variation constant so okay to solve for k so subtitling of course 24 at young x 9 6 so that is 24 is equal to k 6 or 24 is equal to 6 k so paramount sold nothing on k divide both sides by what divide both sides by six okay so 24 divides six k is equal to four e big sub b hand you know variation constant theta is four so balik equation of variation constant y is equal to x okay another example find the constant of variation and the equation of variation in switch in which y values directly as x and y is equal to 51 when x is equal to three so again so translate moon and nothing into equation so y varies directly as x so that is y is equal to k x and then solved for k substitute magnetic value now y and x so our y is 51 and x is three or 51 is equal to three k so to solve for k divide both sides by three so 51 divide three the answer is 17. so eric's opinion constant nothing is seventeen so balik tayden's equation nothing okay nothing and seventeen so therefore equation no no variation not an i y is equal to 17 x okay another example so the table below shows the number of hours t traveled and the distance d traveled by a car find the constant of variation and the equation which describe the relation so dito given a menu table of values spanning that including your constant and equation of variation so first of course in savvy donor this is the distance no the number of rst troubled and the distance traveled by a car so nothing it is okay so d is equal to kt okay it is or 80 is equal to two k so to solve for k divide both sides by two so eighty divide two the answer is forty e big sub in your constant not in d to i four t therefore your equation attends a barbaric okay for example number six if x values directly as y and x is equal to 35 when y is equal to 7 what is the value of y when x is equal to 25 so the true table of values partitioned is equal to k y so x varies directly as y and then substitute nothing you're given at n so your x nothing is 35 and you can you y naught and seven or 35 is equal to 7k to solve for the constant or the value of k divide both sides by seven so the constant is five so balik ties the equation at all so into number five so x is equal to five y situation equation not n so on constant five your equation in volume 25 union volume and y so gamma 2 equation at all so subtitles which is 25 so 25 is equal to 5y sold for y so to solve for y divide both sides by five so y is equal to 25 divide five therefore y is equal to five so up again x is 25 y is equal to five another example if y varies directly as x and y is equal to 24 when x is equal to 6 find the value of y when x is equal to 15. so using the table of values so my kita not n if x is 6 if the value of x is six and the value of y is twenty-four x is fifteen so i'm in volume and y so y only tangent update so nothing so detonating y so y is equal to k x okay again and that including your constant after in a constant nothing equation after an equation is a subtitle so that is 24 is equal to k times six okay so synaptic nothing in volume of y and volume x or 24 is equal to 6k to solve the constant divide both sides by six so 24 divides six the answer is four okay so balikta additional equation at n so you need to are in constant polytechnic and 4 so your equation at it is y is equal to 4x so on tanong if x is 15 what is the value of y so subtitles x not n so y is equal to 4 times 15 so paparita nothing x nothing and 15 therefore if x is 15 y is equal to 60 okay let's have a application of direct variation important direct variation for example number eight a workers paycheck p virus directly as the number of hours each work for working 20 hours the payment is 1000 pesos find the payment for 45 hours of work so nothing in problem so after working 20 hours so baba yala and shannon 1000 so makkah no after working 45 hours so yeah nothing so again kayla not any translation so p values directly as the number of r so that is p is equal to k h and then parameters [Music] is 20 or so 1000 is equal to 20k so nothing convenient constant divide both sides by 20 so 1000 divided 20 the answer is 50. so your constant that indeed so that is okay subtitle nothing equation so 50 times 45 so the answer is 2 250 pesos so eb sub sabihin uh um after 45 hours of work i 2 250 pesos okay another word problem the weight of an object on the moon virus directly as it weight on earth an astronaut weight 80 kilogram on earth weighed 12.8 kilogram on the moon so that is moon okay how much would the 60 kilogram person wait on the moon okay okay so first we need to translate the statement now using the definition of direct variation so that is y is equal to kx problem number and after that replace uh y with 12.8 so papadi nothing and why not in a 12.8 and x with 80. so that is 12.8 is equal to 80k and sold 4k so polynomial k by dividing both sides by 80. so 12.8 divide 80 so the answer is 0.16 ebitda this is now the constant of variation in 0.16 and after that moku won the nothing equation at 10 so baliktayadito malik dijon so in equation and at an i y is equal to 0.16 x so next is use the equation of variation to find y when x is 60 okay so nothing equation and y when x is 60 to your 60 kilogram so replace x with 60. so papa so that is 0.60.16 times 60 the answer is nine point six so it because i'll be in a 60 kilogram person no on earth will weight 9.6 kilogram on the moon okay short time so before we start so mcgrady monarch paper and pen okay i'll give you five questions for the answer for question number one which of the volume represents the statement a varies directly as b a b is equal to k a ah hey no no letter b a is equal to k b letter c a is equal to k over b and letter d b is equal to k over a okay so the answer is letter b a is equal to k b next question number two find the constant of variation in which y values directly as x and y is equal to 28 when x is equal to two letter a one over fourteen letter b one over twenty eight and letter c one uh fourteen letter d twenty eight yes the correct answer is letter c k is equal to 14. question number three find the equation of variation in which y values directly as x and y is equal to 28 when x is equal to 2. number two letter a y is equal to 10 x letter b y is equal to 12 x letter c y is equal to 14 x and letter d y is equal to 16x all right the answer is letter c y is equal to 14x next question number four which an example of a direct variation letter a x y is equal to ten b y is equal to two over x letter c y is equal to five x and letter d two over y is equal to x okay so the answer is letter c y is equal to 5 x next is the last question what happens to t when h is doubled in the equation t is equal to four h t is double b t is half t a letter c t is three pole and d t becomes zero yes the answer is letter a also t is double okay if you get a perfect score congratulation you can share or you can comment your score in our comment section thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel