Hi, my name is Marija and I'm a mathematician and today I'm going to show you how to find the b-intercept or the y-intercept when given 4 coordinates. So if you are told that your line passes through the points (1,2) and (3,6) and you want to find b, you want to find the y-intercept. First, we need to find the slope though so what we're going to do is use these 2 points to find our slope. So slope is always equal to y2-y1 over x2-x1. So I'm going to label these coordinates so you know which is which, if this is my x1 then this y1 and if this is x2 that's y2. So now I'm just going to substitute, y2 minus y1 that means 6 minus 2 which is 3 and then I have x2-x1, 3 minus 1 which is 2 so my slope is 3/2 and the reason I need to find that first is because now in this formula y=mx b, if you're looking for b, if you're looking for b you need the other 3 things. So I've got 2 of them I can pick whichever 2 points I want, I'll take this point, these 2 coordinates and I'll replace y with 2 since my y coordinate's 2, I'm going to replace m now with 3/2 because I just solved for it and I'm going to replace x with 1 and now I'm solving for b because that's what you wanted. So 3/2 times 1 is just 3/2 so I have 2 equals 3/2 plus b and now I'm just going to subtract 3/2 from both sides and when I do that I get b equals and I recognize that 3/2 is the same thing as 1 plus 1/2 so I'm left with a 1/2 so that means that b or my y intercept here is 1/2. So that is how you use 4 coordinates to find the y-intercept or b.
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