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Current time:0:00Total duration:4:37

Identifying constant of proportionality graphically

CCSS.Math: ,

Video transcript

or asked what is the constant of proportionality between y and X in the graph and just as a reminder when we're talking about constant of proportionality it sounds like a very fancy thing but it's not too bad if we're thinking about any XY pair on this on this line let's say right over here we have some X comma Y if Y is proportionate or is proportional to X then that means we can say that Y is equal to some constant Y is equal to some constant times X and that constant that is our constant of proportionality right over there sometimes you will see this expressed if you divide both sides by X sometimes you will see this as Y over X is equal to the constant of proportionality it shows if you for any XY pair if you take your Y divided by X what do you get that's the same same thing so with that out of the way see if you can answer their question what is the constant of proportionality between y and X in the graph well they very clearly give us a point right over here this point is the point 3 3 comma 2 and so we could set it up a few ways we could say look when y is equal to 2 X is equal to 3 and so 2 would need to be equal to some constant of proportionality times 3 and if you wanted to solve for this you just divide both sides by the 3 so divide both sides by 3 and you would get that your constant of proportionality is 2/3 another way to do it right over here well here we've kind of already solved for our constant of proportionality when Y or would you say when X is 3 when X is 3 y is equal to 2 in either case our constant of proportionality is 2/3 let's do another example so here we have which line has a constant of proportionality between y and X of 5 over 4 so pause video and see if you can figure that out so the key realization is we should test points on these lines we should test XY pairs and say well look if we take our Y divided by X do we get 5/4 because that would be our constant of proportionality so let's first try let's fot try line a right over here so line a then we find a point that sits on it so that looks like a point that sits on it and so if I take this is the point 2 comma 5 and so if I took Y divided by X I would get a constant report constant of proportionality as 5 halves so a is not going to be our answer we want to get to a constant of proportionality of 5/4 all right let's try B ok B let me find a point on B looks like this is a point on B that is the point 4 comma 5 4 comma 5 and so in this situation K would be our Y which is 5 divided by our X which is 4 so it looks like B is our choice for kicks you could also look at the constant of proportionality right over here now there is one interesting example that I just want to touch on before we finish these examples what about a situation where Y is equal to X what is the constant of proportionality then and what would it look like as well as a line pause this video and think about it well there's really nothing new here it's just you might not really see the constant of proportionality when you see it express this way but why Y is equal to X is the same thing as Y is equal to 1 times X and so then it might jump out at you that the constant of proportionality is 1 in this scenario right over here or if you took Y divided by X Y over do it in that black color or if you took Y over X you divide both sides by X you would be left with the constant of proportionality which would be equal to 1 and if you wanted to graph it well it would just look like this Y would be equal to X for all X's so that's what when your constant of proportionality is one you would those would represent points on this orange line that I just constructed