 This data table comes from the USGS and it tells you how many earthquakes are given magnitude happen on average every year all over the world. So you can see that there are way fewer really big earthquakes than really small earthquakes and that's a good thing. I like to make a plot out of this data because I think it's more instructive to make a plot. Over here I've already drawn my axes. This is magnitude on the x axis and this is number of earthquakes on the y axis and you can see that I've made a log scale plot here. So this is 10, this is 100 million up here. Why don't we just plot this data from this table onto this and we'll see what it looks like. So how many earthquakes of 8 and higher are there? Well there's about one and that is right about here on my plot. For magnitude 7 it's about 15, that's about here. For magnitude 6 is 134, that's about here. Magnitude 5 is a little bit over 1,000. Magnitude 4 is a little bit over 10,000. Magnitude 3 is estimated to be a little over 130,000. Magnitude 2 is estimated to be a little over a million. Magnitude 1's and anything smaller aren't in this table but I bet we can just extrapolate, can't we? Because if we connect up all these points we have drawn a line. So I can extrapolate that magnitude 1's enough are probably a little over 10 million and magnitude 0's, anything smaller is a little over 100 million. Magnitude is a log scale so it actually is meaningful to have a magnitude 0. Alright, so we've drawn this line and when I was a kid in school I learned that the formula for a line is y equals mx plus b. So why don't we write this formula in terms of what we know about this plot, right? What's y? Well y is the number of earthquakes as a log scale, right? So it's actually log of the number. Slope is rise over run, right? So the rise is actually negative minus 1 unit on our plot and the run is plus 1 unit on our plot. So that's a slope of negative 1 and x is magnitude and the y-intercept is a little over 100 million. It's probably 130 million, right? That's how these numbers are going up so we could just guess on 30 million. So the log of the number of earthquakes equals negative 1 times the magnitude plus 130 million for the whole world for a year. Now, who cares, right? Why are we bothering to write this down? Well the reason is that in fact you will verify in your problem set that this slope is always negative 1 no matter what part of the world it is and no matter what the time scale is. The only thing that changes when you don't look at the whole world annually is that this y-intercept will change, right? Because if you look at say California there's fewer earthquakes in California than the whole world, right? But this line is basically always true. So if you want to predict how often a really big earthquake is going to happen then it's important to keep track of how many small ones happen because then you can draw this line and guess how often the big one is going to happen. That's what you're going to do in your problem set.