Constant of proportionality from graph

- [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.