Hey, everyone. So throughout our discussion on lines, we've seen problems where they ask us to calculate the slope of a line by looking at the rise over the run between two points. But some problems like the one we're going to work out down below won't ask for just that. Some problems will ask us to look at the graph of a line and write its equation in a very specific way called the slope-intercept form. So that's what I want to talk about in this video. And what I'm going to show you is it's basically just a very specific way that we write an equation of two variables using two things we've already seen before independently. So we can use its slope and its intercept, specifically the y-intercept. Alright? So I'm going to show you this equation, and it's probably something that you've seen before. So let's get started.

The slope-intercept form of an equation is actually just an equation. That's y=mx+b. You've probably heard that at some point in a math class, y=mx+b. This is just the slope-intercept form of a line. It's one of the most easy and straightforward ways to describe a line equation. So let's get started and talk about these two variables here. The m is basically just the slope, and we've already seen that before. We calculate that by using ΔyΔx, rise over run, or you can just use the sort of longer format here. So in this equation, what we can see is that the rise over the run between these two points is 2 over 1, and so the slope is just 2. What about the y-intercept? Well, the b term over here is the y-intercept, and we've already talked about that separately. The y-intercept is basically just the y value wherever the graph crosses the y axis, and it's where x=0. So for instance, in this case, the graph crosses the y axis right over here. The y value at this point is 3. So that is the b term. Right? So that's the y-intercept. So to put these things together, y=mx+b, all you have to do is the equation here has a slope of 2, so that goes in front of the x, and then the intercept is 3. So the equation of this line is just y=2x+3. That's how to describe this equation in slope-intercept form. That's really all there is to it. Alright? So that's all there is to slope-intercept form. Let's go ahead and take a look at another example. Alright? So in this graph below, we're going to identify the slope, sorry, the slope and the y-intercept, and then we're going to write the equation in slope-intercept form. So remember, slope-intercept form here is just going to be y=mx+b. In order to figure out m and b, we're going to have to take a look at the graph. Alright? So the always easiest sort of value to start with is going to be the b term because you really just have to look at the graph and figure out where does it cross the y-axis. You don't have to calculate anything. So let's take a look at this graph. Where does it cross the y-axis? Well, it crosses right over here. So what's the y value where this graph crosses the y-axis? It's just negative 3. So that's the b. It's just negative 3. That's all there is to it. You don't have to write the ordered pair. It's just the y value. Alright? So how do we calculate m? Well, for m, we're going to have to use rise over run. So we're going to m we're just going to calculate this by using ΔyΔx. Or if we're given two points, you could just plug those points in. But, basically, if I'm going to have this point ove