Proportionality constant from table

• [Instructor] We're told the quantities x and y are proportional, and then they give us a table where they give us a bunch of x's and they give us the corresponding y's.

When x is four, y is 10. When x is five, y is 12.5, and so on and so forth.

Find the constant of proportionality, r, in the equation y is equal to r times x. So pause this video and see if you can figure that out.

All right, so we wanna find the constant, the constant of proportionality, I sometimes have trouble saying that, r, where if I, for any x, if I multiply it by r I get y.

Well, we just have to look at each of these x's and figure out, well, what are we multiplying by to get to y.

So what do I have to multiply four by to get to 10? Well, if you multiply it by 10/4, if you multiply it by 10/4, then you're gonna get to 10.

And 10/4 is the same thing as multiplying it by, let's see, that is 2 1/2. So this is times 2 1/2.

So let's see, does that hold? In every case, if I multiply by 2 1/2, if I multiply x by 2 1/2, do I get y?

So five times 2 1/2, five times two is 10, and then another 1/2 is 2.5. It indeed does equal 12.5.

Five times 2.5. And then here, 10 times 2.5 is clearly 25.

And you can work it out by hand. I did a little bit of the multiplication in my head, but you can see in every case, I take my x, I multiply it by 2.5, I get my y.

So in every case, I take my x and multiply it by the constant of proportionality 2.5, I get my y.

So what's the constant of proportionality? It is 2.5.