Writing a linear equation

Welcome to linear math. Today we're going to learn how to find the equation of a line if you're given two points. So our two points are three one and 7 four. And we're going to write the equation in the form Y equals MX plus B, which is our slope intercept form. So for an equation, we need to pieces of information. The first one is M, which is our slope. And the second one is B, which is our intercept. So let's go through and find each part. For slope, you're going to use your slope equation. Y two minus Y one over X two minus X one. So let's subtract our Y's on top, four minus one, four, minus one, over, and if I use the four first, you 7 first, 7 minus three. So that gives me a slope of three, fourths. Okay, so that's the first step is to find the slope. Now let's find the intercept. Now there are two ways to do this. The first way I'm going to show you is just using the form Y equals MX plus B and using the slot we just found and then one point to solve for B so let's plug in, we can pick either point either three one or 7 four. I'm going to pick three one. So I'm going to use the .31 and the slope of three fourths and so I'm going to plug in for Y I'm going to plug in a one for M that's a slope I just found that I'm going to plug in a three fourths and for X I'm going to plug in positive three. And I'm going to solve for B so now I'm going to multiply three fourths times three when you take a fraction times a whole number, stick a one under it and then just multiply top and bottom so that gives me 9 fourths plus B is equal to one and then I have to subtract 9 fourths from both sides. Now if you remember when you have a whole number minus a fraction, I've got to write this whole number as a fraction with a denominator of four. So that's going to be four fourths. Anything over self is one. So four fourths to -9 fourths is negative 5 fourths. And that is my value for B so once I simplify that, I can now use my B and my intercept, which I mean my slope, which is three fourths and write my equation. So I plug in Y equals and my slope is three fourths. Leave the X as your variable and then plug in B as negative 5 fourths. And that's how you write the equation of a line, given two points. Now you can use a second equation. Once you find your slope, if you want to use Y minus Y one equals M times X minus X one, you can plug in for the X and Y and the slope into this equation, and then simplify that one also. That is called a point slope equation where you have a point and the slope and you plug in and you just simplify that. So hope this video was helpful and giving a couple options to find the equation align given two points.