Master the Gradient How to Find the Slope of a Line

Hello everyone. In this video, would like to show you how to find the gradient or the slope of line. We will do find the gradient from two points just like this question here. Find the slope of the line passes through these points. We will also learn how to find the slope from the equation of the line such like this question here. And we will also learn how to find the gradient or the slope from graph like this one. We will learn all. All right. So let's just start from two points. How do we find the gradient from two points? So the question usually looks like this. Find the slope of the line passes through 2 and -4 and 6 and 1. To do this, you will first need to know the formula. It's the difference in y's divide by the difference of It can be y1 - y2 / x1 - x2. Some teachers they say it's y2 - y1 / x2 - x1. It's both correct. What's important is the y's should be up and the x's should be down. Another important thing is if you start by the y's by y1 down here you should start by x1 and if you start by y2 you should start by x2 in the denominator you can't do y1 minus y2ide by x2 - x1 this is wrong if you do x2 - x1 so you start by y1 you start by x1 so you can use this or this now let's of solution of this example. The first point is 2 and4. Let's just call it x1 and and y1 because it's the first point. And the second point is 6 and 1. So it's x2 y2. Now just substitute the values. Y1 is -4. Y2 is 1. X1 is 2. X2 is 6. We can just put them -4 -1 / 2 - 6. So, y1 - y2 / x1 - x2. If you use this one, it's the same thing. The numbers will just change. Y2 the position will change. Y2 is 1, y1 is -4, x2 is 6, x1 is 2. So it will just be 1 - -4 / 6 - 2. Now -4 - 1 is - 5. 2 - 6 is -4. So it's - 5 / -4 which is just 5 / 4 because negative by negative is positive. Here 1 - - 4 is 5 / 6 - 2 is 4. So it's also 5 - 4. So it's the same thing. If you use the first rule or the second rule, it will give you the same gradient or slope. Now let's look at this example. You can pause and try it. I'll first write the formula. The first point is x1 y1. The second point is x2 y2. With the values y1 is -2, y2 is 5, x1 is 3, x2 is five. So it will just be something like this. Now -2 - 5 is - 7 and 3 - 5 is -2. So it's just going to be 7 / two. And here it's going to be 5 + 2 / 2 which is 7 / 2. So it's the same thing. It's up to you. You can use the right side or the left side formula. It's the same thing. Now let's see how we find the gradient from the equation. By the way, the gradient and slope, it's the same word. It's the same thing. They sometimes ask you to find the gradient. They sometimes ask you to find the slope. It's the same thing. Now, from the equation, we'll first need to remember the equation of the line. It's = mx + is the gradient or the slope. This is what we want. So, the question can be direct like this one here. Any of these = 3x + 5, = -3x + 5, = 2 over 3x + 5, = -2 over 3x + 5. The gradient is just what comes in front of the What comes in front of the is is the slope is the gradient. So in this example, it's just 3 -3 2 over 3 -2 over 3. These are easy examples and it's usually not in the exam. What can be in the exam is something like this. = + 5 y=x + 5. This is confusing for many of the student. The students don't see any number in front of the So they say the gradient is zero. It's not. If it's it's 1 isn't it? So the gradient is just one. If it's negativex, it means -1. Sorry, it means it's -1x. So the gradient is -1. So here it's one and is -1. So remember this is very important. Now let's have look at some challenging examples. If let's just move this. If the question says = - 3x = 5, what's the slope? Now, we first need to make it look like = mx + So, we need alone in one side and everything else to be on the other side. We can't say the gradient is -3. No, we must make it look like = mx + Now to do this I'll need to move the 3x - 3x to the other side. I'll do + 3x on both sides to cancel this 3x. So the 3 - 3x cancel the + 3x. On the left side we just have On the right side we have 3x + 5. Right? This 3x and this five. So now it looks like = mx + and is just what's in front of the So it's just three. So if the if the question is not in this formula, you first need to make it look like this and then tell what's the gradient. Let's have look at another example. What if it was 2y - 3x = 5? We need it to look like = mx + So will first get rid of this minus 3x. How do get rid of it? do + 3x. The minus 3 and + 3 they will cancel. So on the left side I'll just have 2 On the right side have 3x + 5. This 3x and this five. It's not yet in this formula. So I'll divide everything by two. So divide everything by two. The two cancels the two. So on the left side I'll just have On this side I'll have 3 over 2x + 5 / 2. Now the gradient is what's in front of the So it's just 3 over two. Again slope and gradient is the same word. Now it's your turn. It's very important to practice. Practice makes better. Can you please try this one? Comment your answer. What's the slope? What's the gradient? Give it try and let's see. Now, let's go to the last part. From the graph, how do we find the gradient from the graph? The question will look something like one of these. They will give you line. They ask you to find the slope or the gradient. Let's do the first one. To do this, you will first need to know what's the gradient. What's the slope? It's rise over run. It's not rise, it's rise over run. So the slope is rise over run. What's even rise and run? This is confusing for many of the student. Let's make it easy. Let's make it easy. The first thing you need to do is to pick two nice perfect points. Here they are given. They gave us these two points. But let me explain. If these points are not given, how do you find it? So this is point on the line, the red one. This is another point. This is another point. point. point. So we did all these points. Now, which point should we choose? If you look at this point here, it's very good. It's nice point because it's on the cross. It's on point like the cross of the and Something like this. This is perfect point. Now, if you look at the second point here, it's not on cross. It's just in the middle of this line here. So, it's not perfect point. Now, every not perfect point. You don't need to look at. Now, this is not perfect point. This is also not perfect point because it's not on cross of line. Now, these three points are not perfect points. So, I'll just drop them away. Now, we have four perfect points. You can choose any. I'll choose these two perfect points. I'll now think of going from here to here. can't just go like this. need to rise and then run. So, how many steps do we rise? We rise up one step. And to go to the other point, we run two steps. Did you get it? If you don't think of you are driving and you're going from here to here, but you can't go on the line, you need to go up and then you need to run. So we rise again, one step up and we run one, two steps. So the slope is rise over run. So it's one over two. Do you get it? Now let's go and have look at another example. We did this one. So let's do another one. Let's do this again. The gradient is rise over run. From this point to this point, how do we go? We go down two and we run two. When you go down, it's negative because you didn't rise. You go down. So it's -2 over two, which is just -1. Let's have look at this example. This is challenging one. This is tricky one. Now, let's choose two perfect points. Is this perfect point? No, it's not. Why? Because it's not on cross. It's not like on these points. It's somewhere in the middle. So, this is not perfect point. Did you get it? The perfect point should be on the cross on corner. Now this is not perfect point. So let's choose two perfect points. These two points are nice are perfect. This is good point. This is good point here. So from this point to this point how many steps do we rise? We rise here. Now many students will say we rise one two. It's not two because this is from zero up to 10. We rise 10 steps. And many students will say we run one step. No, it's not one because look from here to here it's two because it's 0 to two. So it's two. This is the run. It's two. Now the slope is rise over run. So it's 10 of two which is just five. Do you think you understand? 0 10. Can you please find the slope of this line? Write your answer in the comments and please do not forget to like and subscribe. That's all for this nice video. Thank you for following. Bye.