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- [Instructor] 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. All right, 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 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 zero, y is zero. But if I multiply zero by
anything, I'm gonna get zero. But then when x is one, what is y? When x is one, y is three. They mark it right over there. When x is two, what is y? X is two, we see that y is six. So our constant of proportionality is what are we multiplying x by to get to y? Well, let's see, to go from one to three, I have to multiply by three. To go from two to six, I
have to multiply by three. 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 three, you get your y. So the relationship here
is y is equal to three x. So three is our constant
of proportionality.