In this video, we're going to talk about how to find the slope and y-intercept from a linear equation. Now, it's important to be familiar with the slope-intercept form of a linear equation, and here it is. m represents the slope. m is the number in front of x.
b represents the y-intercept. So if we were to write the slope-intercept equation right below this one, we can clearly see that m, which is the number in front of x, that's 2, and b is the constant, that's 3. So in this problem, the slope, which represents m, is 2, and the y-intercept. which is equal to b, that's 3. So that's a quick and simple way of how you could find the slope and the y-intercept from the equation. However, not all examples are as simple as this, so we're going to cover a lot of examples in this video.
Go ahead and try these two examples. Let's say y is equal to 3 over 4x minus 5 and also y is equal to 8 minus 4x. So feel free to pause. video and try those examples if you want to. So for number two we can see that the slope is just the number in front of X so the slope is going to be 3 over 4 and the y-intercept is the number other than this.
It's the constant without the x. So it's negative 5. Now for the next example, it's not written in slope intercept form, but we can change that. If we were to switch to 8 with the negative 4x and write it this way, we get negative 4x plus 8. Keep in mind, there's a plus in front of the 8. You just don't see it immediately. So writing it this way, we can see that the slope is negative. 4 and the y-intercept is 8. If it's not given to you in slope-intercept form, you need to adjust the equation and put it in slope-intercept form.
Once it's in slope-intercept form, you could find the slope and the y-intercept. Go ahead and try these two examples. Let's say we have y is equal to 5 minus x and also y is equal to negative 7x. So for the fourth example, I'm going to reverse or switch to 5 and the negative x. So this is negative x plus 5. Now you might be wondering, what is the slope here?
We don't really have a number. If you don't see a number there, assume it's always a 1. So this is negative 1x plus 5. That's the same as negative x plus 5. Therefore, the slope for this line is negative 1, and the y-intercept is 5. So that's it for number 4. Now what about number 5? All we have is just a negative 7x.
It doesn't appear to have any b-value. In a situation like this, you can rewrite this equation as follows. So y is equal to negative 7x plus 0. Negative 7x plus 0 is the same as negative 7x.
And writing it this way, you can clearly see that the slope is negative 7, but the y-intercept is 0. So that's all you need to do for that particular example. Now what about these two? Let's say if we have y is equal to 3 and x is equal to 4. What is the slope and y-intercept for these two lines? I want you to think about that for a moment. Now for y equals 3, we can rewrite this like this.
We can say it's y is equal to 0x plus 3. So this is in slope in the subform. 0x plus 3 is equal to 3. These two have the same value. So we can clearly see that m is 0. And b is 3. So for this problem, the slope is 0, and the y-intercept is 3. Now what about for x equals 4? Because you can't really put that in slope-intercept form.
So what do you do to get the answer there? For x equals 4, you need to graph it. y equals 3, this is a horizontal line at 3. Horizontal lines, they have a slope of 0. Because they don't go up, they don't go down, they're just flat.
And you can see the horizontal line, it touches the y-axis. This is the x-axis, this is the y-axis. It touches the y-axis at 3, so that's why the y-intercept is 3. because that's where it touches the y-axis.
Now for a vertical line, x equals 4, the situation is different. So this is how we can graph x equals 4. It looks like this. For vertical lines, there is no slope.
If you try to calculate the slope of a vertical line, it's going to be undefined. If you're wondering how you can calculate the slope of a horizontal or vertical line, you could use this formula. m is equal to y2 minus y1 over x2 minus x1. So for the horizontal line, if you pick any two points, Let's say this is y1, y2.
In both cases, y1 and y2, they'll have a value of 3, regardless of what x1 and x2 is. And so it's always going to be 0. All the y values on a horizontal line will have the same y value of 3, because y is 3, it's always 3, anywhere on this horizontal line. So this is always going to be 3 minus 3 for this line, giving you a slope of 0. Well, for a vertical line, x is always the same.
So these two points may have different y values. This may be y1, y2, but the x value is always 4. And so if you were to calculate the slope using this formula, it will be y2 minus y1, but on the bottom, x2 and x1, they're going to be 4. And so you're going to get a 0 on the bottom. Whenever you have a zero in the denominator of a fraction, it's going to be undefined So for a vertical line, the slope is always undefined. Now what about the y-intercept?
Now this vertical line, will it ever touch the y-axis? The answer is no, because it's parallel to the y-axis. So it will never touch the y-axis. Therefore, for the y-intercept, there's none.
There is no y-intercept. So whenever you see an equation like this, x equals some number, the slope is going to be undefined and the y-intercept is just going to be nothing. There's no y-intercept. By the way, for those of you who want access to more video-related content, feel free to check out the links in the description. If you click on this More button, you're going to see other videos relating to the video that you're currently watching, and these links are separated by chapter.
And of course, you can check out my website, video-tutor.net, where you'll get access to my video playlists, final exam videos, and also test prep videos. So feel free to take a look at that when you get a chance. So let's say if we have y equals negative 6 and x equals negative 2. So whenever you have y is equal to some number, whether it's a positive or a negative number, the y-intercept is going to be whatever y equals, and the slope is always going to be 0 for this kind of line. Whenever you see x equals a number, whether it's positive or negative, the slope is going to be nothing.
I mean, the y-intercept is nothing, but the slope is going to be undefined. It's always going to be that way, based on the explanation that I gave you for the last time. examples now what would you do if you get a linear equation in this form so right now this linear equation is in standard form and in order to determine the slope and the y-intercept we need to put it in slope intercept form y equals mx plus b So the way to convert it from standard form to slope intercept form is you need to solve for y In other words you need to get y by itself on one side of the equation So first we need to get rid of this 2 in front of y and this term we need to move it to the other side So what I want to do is get rid of the 2 first I'm gonna divide everything by 2 So negative 4 divided by 2 is negative 2. 2 divided by 2 is 1, so 1y is the same as just writing y.
And 6 divided by 2 is 3, so we have this. Now, I'm going to take this term, move it to the other side. On the left side, it's negative 2x.
When I move it to the other side, it will be positive 2x. The other way to do this is to add 2x to both sides. If you add 2x to both sides, this will cancel here.
And we'll get y is equal to 2x plus 3. As you can see, if you simply move it, it changes from negative 2x on the left to positive 2x on the right. And we can see that the slope is 2 and the y-intercept is 3. So that's it for this example. Let's try a somewhat similar problem. Let's say we have 3x minus 5y is equal to 8. Go ahead and find the slope and the y-intercept for this line.
So first, I want to get rid of the number in front of y. So I'm going to divide both sides by negative 5. So I'm going to have negative 3 over 5x. These two will cancel, so I'm just going to get plus y. Negative 5 divided by negative 5 is positive 1. And then this equals negative 8 over 5. Now I'm going to take this term and move it to the other side.
So I'm going to get y is equal to, it's negative on the left, but it's going to be positive on the right. So positive 3 over 5x, and then minus 8 over 5. So this is my m value. m is the number in front of x, m is 3 over 5, and this is my b value. b is going to be negative 8 over 5. So now I have the slope and the y-intercept. Now let's work on one more example.
Let's say I have negative 2 over 7x plus 3 over 7y is equal to 4 over 7. So what should we do to convert this standard equation into its slope-intercept form? What would you do? Now, just like before, I want to get rid of the 3 over 7 in front of the y.
But if I divide everything by 2 over 7, that can make the math a bit complicated. So because I have fractions, and I want to get rid of the fractions, I'm going to multiply everything by 7. Doing this, all the 7s will cancel with this 7. So I'm going to get negative 2x plus 3y is equal to 4. Next, I'm going to get rid of the 3 in front of the y by dividing everything by 3. So I'm going to get negative 2 over 3x. 3 over 3 is 1, so this is just going to be plus y is equal to 4 over 3. Then I'm going to take this term and move it to the other term. other side and I'll get y is equal to positive 2 over 3x plus 4 over 3 and so I could see that the slope is positive 2 over 3 and the y-intercept is 4 over 3 So that's how you could find the slope and the y-intercept from a linear equation.
All you have to do is convert it to slope-intercept form and identify your m and b values. So that's it for this video. Thanks for watching. For those of you who want more videos on algebra, linear equations, feel free to check out the links in the description section below. Thanks for watching.