 Okay, can you hear me? Hold on. Yep. Okay, cool, I can hear you too. So take a look at this. In, in, oh, let me take this off too. So in grade 10, right? You guys did mathematics and in grade 11, we talked about this as well when we were doing math, right? We said Y is equal to MX plus B, right? That was an equation of a line. Do you remember this? Okay, M is your slope and B is your Y intercept, right? You know what these means? Are you okay with this? No, the Y intercept is when the line crosses the Y axis. So basically it's this, right? If I give you this line, this is the Y intercept, right? And the slope is rise over run. So the slope, the equation for slope is is equal to M, which is rise over run. Can you see this? Is this big enough? Yeah. It's rise over run. Rise over run means, if you start off at a certain point, rise goes up. So this is rise and run is this. Okay. So whatever the distance is from here to here is called rise and whatever the distance is from here to here is called the run. Yeah, yeah, yeah, copy the stuff down. Okay. Okay. Now, how do you figure out a distance from one point to another point? What's the distance from 13 to 20? Seven point. How did you figure that out? Now think about this. The reason you knew it was seven is because your mind is super powerful, right? It can do relations, it can find patterns, and it has memory. Your mind knows how to do the calculations for small, simple numbers, right? So if I ask you what the distance is from 13 to 20, your mind automatically does that because that's familiar to you. But if I say it was the distance from 155 to 420, that's a little bit more difficult, right? So you need to know how to do it for simple numbers and mathematics allows you to extrapolate that same technique to other numbers, right? Math is scalable. Whatever you do for simple mathematical equations you also do for larger ones, right? The rules don't change. So how did you go from 13 to 20? To find the distance between two numbers, take the bigger number, subtract the smaller number. 20 minus 13 is seven. That's how you did it, right? So how do you figure out the rise of this from here to here? How do you figure out the distance from here to here? You take the, because on a coordinate system, if I ask you what the coordinates are there, that's x and y, right? It's two dimensional. This is your x-axis, right? This is your y-axis, agreed? So to be able to put a point on a graph, you need an x and a y, okay? The x tells you where you are along the x-axis. The y tells you where you are on the y-axis, right? So if you want to figure out what the distance is vertically, you're talking about the y's, right? And that y is this number, and this y is this number here. We'll call this y1, we'll call this y2, right? So the rise, how do you figure out the distance from here to here? What's the equation to figure out the distance from here to here? So to figure out the distance from here to here, you have to know this y and you have to know this y, right? So if this was, so how do you figure out the distance from 20 to 13? Subtract, so how do you figure out the distance from there to there? Subtract, that's the bigger number, y2 minus y1. We don't care what it is, whatever it is, because this is generic, right? So the rise is y2 minus y1, and the run, the run is talking about the x-value, right? The run is the x-value because that's this way, right? So how do you figure out the distance this way? Well, you go, your x1 is this guy here, right? From here to here, agree? And this number here, x2. So how do you figure out the distance from there to there? How do you figure out what the run is? Yeah, subtract what? x2 from x1, because this is a bigger number, right? x2 minus x1. This is a slope, you did this like four years ago, I guess now, right? So easy, so easy, and it will come back because it's in your memory. Now, keep in mind, math is symmetrical, right? So basically the way you remember this is you say the slope of something is just rise over run, and how do you figure out rise? That's the y, so you just got to subtract one y from the other y. It doesn't necessarily have to be the big one from the small one, it could be small one from the big one, right? But math is symmetrical, so if you put this guy, the first number to be y2, that number has to be x2, okay? So what you have here is, this point here is, is x1, y1, right? x1, y1, and this point here is x2, y2. So if I ask you to give me the distance, give me the slope for any two points, any two points, you don't even have to have a graphical representation. What if I ask you to give me the slope for negative two and five and four and negative seven? How would you find the slope between these two points? Subtract, subtract what from what? You wanna find the slope, the m, which is rise over run, right? What's the rise? How do you find the rise? Subtract the, yeah, the y values, the y values go up top because that's vertical, rise, right? So what would I write? Minus negative seven divided by, so negative two, yeah. Yeah, right? So, well, I'll check this out. What's a negative and a negative? Positive, so these guys are positive, so your slope, yeah, this is like this. So this becomes, this becomes five plus seven is 12 over negative two minus four is negative six, right? So the slope is 12 divided by negative six is negative two. Well, no, negative two. It has to be negative because the bottom's negative, right? I was just doing the math, you didn't mean that, right? So what can you tell me about this if the slope is negative? If you read those questions again in your assignment, if the slope is negative, then it's inverse, I guess the way they were wording it, it was an inverse relationship, right? It's also sloping down. Right? No, maybe like this, going down because that's a negative slope, that's a reverse. Are you okay with this? You sure? Do you want to take a screenshot of it or anything? Okay, okay, cool, you got it. Yeah, write an example. Whenever you want to learn a method of mathematics, write the example, right? Examples are huge, huge. Yeah, repetition helps, right? Okay, now keep this in mind. Are you okay with this so far? Yeah. Now, the way the question that you did, the way they worded it, this is the way they taught it to you in grade 10, but the way they worded it, they changed things around a little bit. So I'm going to erase this. I'm going to keep this here, ready? Okay, let me rewrite this again, right? So the way you've learned it in grade 10 and 11 in high school basically is y is equal to mx plus b. Y is equal to mx plus b, right? Agree? Now we know what m is, now we know what b is. The way that question was worded was this. Y is equal to b, they didn't even write it as b. They wrote it as a plus bx, right? And they said b is equal to slope and b is less than, oops, b is less than zero, right? So right away, they're telling you b is negative. So b is changed from this b, right? Which is, they're using the wrong, like everybody going through high school learns it this way. Everybody in Canada going through high school learns it this way. As far as I know, everybody in the United States learning the equation of a line goes through this way. But this econ course is given you to this way. So right there, you have to have your guard up, right? They tell you b is negative right away, but that's positive. So you've learned when m is positive, it's going like this. When m is negative, it's going like this. It's a downward slope, right? So when m, when the slope is positive, it goes like this. So let's just say m positive. And when the slope is negative, it goes like this, right? Now these guys are saying b is the slope now. So what you have to do is completely adjust your thinking from here, not completely, but you have to think about the slope as b, b and b. And what you need to do is adjust your original equation that you learned from. You did three years of math on and do it like this, right? So the first question was, what was the first question? Was b negative or something? Whatever it was, right? So does this make sense? Okay, yeah. So what you've learned in high school is there. It's the core essence of what you're being taught, but they may rearrange things, okay? So are you okay with this lab, this assignment you had? Okay, what else? What are the questions you have? Oh yeah, let's plug it in. So, y is 10, right? So 10, we're going by this equation, right? What is the value of x, right? So they're asking you here, what's x? If y is 10, right? Let me write this down. They're basically asking you, what's x if y is equal to 10? And then what was the other ones? Bring back that screen. What is it? b, b is negative 0.75. And a is 40, right? So in mathematics, the name of the game is if you have one unknown, you need one equation to solve it. If you have two unknowns, you need two equations to solve it. If you have three unknowns, you need three equations. Four unknowns, you need four equations, so on and so forth, right? So right now, in this equation that they've given us, there are four variables. y, a, b, x, right? They're giving the values for three of them. That means one of them we're not going to know. And if we plug in these values for the three wherever they belong, we can solve for the unknown because we have one unknown and without one equation. So all you do is just plug in the values, right? So 10 is equal to a is 40 plus b is negative 0.75. Negative 0.75 x. Are you okay with this? So all you do now is solve for this. I would bring the 40 over minus 40. So that's negative 30 is equal to negative 0.75 x. So what do you do now? So have you forgotten how to do this? Let's do this more in depth. I'm going to erase some of these, okay? Okay, let's erase those. Let's make a little bit of more room, all right? So they gave us y is 10, b is negative 0.75 and a was 40, right? Okay, and we don't need this anymore because we know this, right? Actually we'll leave it up there. So basically plug in these values. So 10 is equal to 40 because a is 40 plus b is negative this. Negative 0.75 and x, right? So basically when you want to solve for something, it means get whatever variable is here in the equation, whatever letter you have left over by itself or whatever you're trying to solve for by itself, right? So what we need to do is get x by itself. So when you're trying to get x by itself, what you got to do is do the opposite of bed mass, right? Because when you're simplifying, when you're crunching terms, you do bed mass, which is brackets, exponents. Remember this, bed mass, bed mass, right? So brackets, exponents, division, multiplication, these have the same weight, addition, subtraction, these have the same weight, right? You do bed mass when you're crunching, right? But when you're solving, you do the opposite of bed mass. You do subtraction addition first, multiplication, division, and then exponents and brackets. So you go this way. When you're crunching, you go this way. When you're solving, you go this way, right? And crunching basically simplifying means they give you an expression, there is no equal sign in the question and you're just simplifying, right? So we've got to get rid of, we've got to undo what's being done to the X, right? So how do we undo what's being done to the X? Well, before we can get to the X, we have to get rid of the 40 on this side. How do you get rid of 40 on this side? Yeah, subtract 40, subtract 40. Now, I like to reduce the things I do, but I like it to be visual. So instead of subtracting 40, I just go like this, grab it and draw an arrow over. And if I jump over an equal sign, the sign changes. That's subtraction you're adding, right? Yeah, so what is it? Yeah, exactly, right? So 10 minus 40 is negative 30, right? And what we got left here is negative 0.75X. So we're still trying to get X by itself, right? What's being done to the X here? Multiply it by negative 0.75, right? So to undo something, you got to do the, exactly, you got to divide, you got to, exactly, you got to divide it on both sides. So to undo something, you got to do the opposite of what's being done to it. And the equal sign says if you do something on one side, you got to do it to the other side. So divide this side by negative 0.75, divide this side by negative 0.075. You're okay with this? So this kills this. What's negative divided by negative? It's positive, right? So, yeah, they cancel each other out. So what's 30 divided by 0.75? Use a calculator if you want. So X is equal to, what is it? We can do it manually, but I don't want to bring fractions into this yet. Let's cover the basics, 40. And that was what the answer was, right? I agree, does that make sense? Yeah, if you want to take a screenshot of it or something, that way it's all there, it's like notes for you, right?