Hey, everyone. So in earlier videos, we saw the slope intercept form of a line, y=mx+b. And usually, we use this form whenever we were given information about the slope and intercept and asked for the graph of the equation or the other way around. So, for example, we were asked to graph something like y=23x-1. What I'm going to show you in this video is that sometimes you might be given an entirely different set of information. You might be told something like a slope, and then it passes through some point. So when you're asked to write an equation of a line that passes through a point that is not the y intercept, I'm going to show you that we actually use a different form of writing an equation called the point slope form. Now I'm going to show you the differences and similarities between the two equations. So let's go ahead and get started here.

Again, I first want to talk about when you use these two different forms. We use y=mx+b whenever we're given information about m and b and ask for the graph or the other way around. So, for example, 23 x minus 1, we're given the m and the b, and we're asked to graph it. And we can see how to do that very quickly here. We just know that it's going to pass through the point (0, -1). That's the y intercept, and then we just sort of graph the next point by using rise over run. The slope is 23, so you go up 2 over 3. And, basically, this line is going to look something that looks like this.

Now let's take a look at the equation example that we're going to figure out to solve here, which tells us that we're going to have to write the equation of a line that has a slope of 23, and it passes through some random point (3, 1). So, basically, whenever you're given information like this, whenever you're given the slope like we have here and some random points, which is going to be something like x1, y1, then you're going to use this new form called the point slope form. You also could be given 2 points of information like x₁y₁ and x₂y₂. Alright? So that's the times where you're going to use this new point slope form. And, basically, it's y-y1=m(x-x1). So, really, with this equation, there are three numbers that you need to plug into this equation because these y's and x's actually don't get replaced with numbers.

And so the reason we call it a point slope is because x1 and y1 really are just a point that it's giving you. So let's get started here with part a. We're going to write the equation in this new form. So I'm going to take this equation here, y-y1=m(x-x1). I first need the slope of the line, and so I'm going to go ahead and figure that out first. And we actually already told directly what the slope of this line is. It's just 23. So we already have what that number is. So now all we need to do is just figure out the x1 and the y1. So what is that? Well, really, it's just the point that they're telling you that it passes through. When they say that it passes through the point (3, 1), what they're saying is that this line is going to pass through this point on the graph over here. That's just a coordinate. It's just they're really just giving you the x1 and y1 that you plug into the equation. So it's real... y-1=23(x-3) So this is the equation in point slope form of the line that passes through this point over here and has a slope of 23. That's it. That's the point slope form