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the following graph shows a proportional relationship what is the constant of proportionality between y and X in the graph pause this video and see if you can figure that out alright now let's do this together and let's remind ourselves what a constant of proportionality even is if we know that there is a proportional relationship between y and X then there will be a constant of proportionality between these variables and what this is is is it is a number that I would have to multiply X by to get to Y so I could make a little table here as we often do when we describe proportional relationships x and y we know that when x is 0 Y is 0 but if I multiply 0 by anything I'm gonna get 0 but then when x is 1 what is y when X is 1 Y is 3 they mark it right over there when X is 2 what is Y X is 2 we see that Y is 6 so our constant of proportionality is what are we multiplying X by to get to Y well let's see to go from 1 to 3 I have to multiply by 3 to go from 2 to 6 I have to multiply by 3 another way to think about it is we could write the equation y is equal to something times X the number that we multiply X by to get Y is our constant of proportionality and we've seen in all of these situations this should be true for any point on this line you give the X you multiply it by 3 you get your Y so the relationship here is y is equal to 3 X so 3 is our constant of proportionality