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# Identifying proportional relationships from graphs

## Video transcript

we are asked how many proportional relationships are shown in the coordinate plane below and we have the choices but let's actually look at the coordinate plane below to think about how many proportional relationships are depicted here so pause this video and try to answer that yourself so let's do this together so if we're thinking about a proportional relationship or the graph of a proportional relationship there should be two things that we're looking for one it should be a line it should be a linear relationship between the two variables Y should be some constant some proportionality constant times X so you immediately would rule out our green curve here because this is not a line you don't have a constant relationship between Y being some proportional at Y being some proportionality constant times X and for the same reason you would rule out this blue curve now what about this Purple Line this might be tempting because it is a line but it does not go through the origin when X is 2 y is 0 times X while when X is 4 y is 1 times X and when X is 6 Y looks to be 1 and 1/3 times X so you don't have the same proportionality constant the entire time so we have 0 proportional relationships depicted here so I would pick 0 there let's do one more example natalie is an expert Archer the following table shows her scores points based on the number of targets she hits all right targets hit and then the points she gets plot the order pairs from the table all right so the first one is 1 comma 3 so here I'm doing it on Khan Academy my horizontal axis is target's hit and my vertical axis is points so one target hit three points so this is going to be one target hit this is going to be three points then I have two targets hit six point so two targets hit and I have six points and then I'm gonna have through or five targets hit fifteen points so then I'm gonna have going to have five targets hit and that is going to be fifteen points and so this is looking like a proportional relationship in every situation my points is equal to three times the targets hit so my proportionality constant is three and you can see if you try to connect these dots with a line it will be a line a line can go through all three of these and it will go through the origin so our nataly's points proportional to the number of targets she hit yes absolutely