Here 'm' is the slope of the line and 'b' is the point at which the line intercepts the y - axis. A line for which the slope in negative is said to move from left to right in a graph. The slope of a line is found by the ration of difference in y-coordinates to the difference in x-coordinates. If this value is negative for a line, then the line has a negative slope. The direction of a line is described by its slope.
The slope can be positive or negative, based on its direction. A negative slope moves downward from left to right and a line with positive slope moves in the upward direction from right to left. Learn Practice Download. Have questions on basic mathematical concepts? Become a problem-solving champ using logic, not rules. Learn the why behind math with our certified experts. How to Find the Slope of a Line?
What Does the Slope of a Line Mean? Explore math program. Explore coding program. Make your child naturally math minded. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Voiceover] There's a lot of different ways that you could represent a linear equation.
So for example, if you had the linear equation y is equal to 2x plus three, that's one way to represent it, but I could represent this in an infinite number of ways. I could, let's see, I could subtract 2x from both sides, I could write this as negative 2x plus y is equal to three. I could manipulate it in ways where I get it to, and I'm gonna do it right now, but this is another way of writing that same thing. You could actually simplify this and you could get either this equation here or that equation up on top.
These are all equivalent, you can get from one to the other with logical algebraic operations. So there's an infinite number of ways to represent a given linear equation, but I what I wanna focus on in this video is this representation in particular, because this one is a very useful representation of a linear equation and we'll see in future videos, this one and this one can also be useful, depending on what you are looking for, but we're gonna focus on this one, and this one right over here is often called slope-intercept form.
Slope-intercept form. And hopefully in a few minutes, it will be obvious why it called slop-intercept form. And before I explain that to you, let's just try to graph this thing. I'm gonna try to graph it, I'm just gonna plot some points here, so x comma y, and I'm gonna pick some x values where it's easy to calculate the y values.
So maybe the easiest is if x is equal to zero. If x is equal to zero, then two times zero is zero, that term goes away, and you're only left with this term right over here, y is equal to three.
Y is equal to three. And so if we were to plot this. Actually let me start plotting it, so that is my y axis, and let me do the x axis, so that can be my x, oh that's not as straight as I would like it.
So that looks pretty good, alright. That is my x axis and let me mark off some hash marks here, so this is x equals one, x equals two, x equals three, this is y equals one, y equals two, y equals three, and obviously I could keep going and keep going, this would be y is equal to negative one, this would be x is equal to negative one, negative two, negative three, so on and so forth.
So this point right over here, zero comma three, this is x is zero, y is three. Well, the point that represents when x is equal to zero and y equals three, this is, we're right on the y axis.
If they have a line going through it and this line contains this point, this is going to be the y- intercept. So one way to think about it, the reason why this is called slope-intercept form is it's very easy to calculate the y-intercept.
The y-intercept here is going to happen when it's written in this form, it's going to happen when x is equal to zero and y is equal to three, it's gonna be this point right over here. So it's very easy to figure out the intercept, the y-intercept from this form. Now you might be saying, well it says slope-intercept form, it must also be easy to figure out the slope from this form.
And if you made that conclusion, you would be correct! And we're about to see that in a few seconds. So let's plot some more points here and I'm just gonna keep increasing x by one. So if you increase x by one, so we could write that our delta x, our change in x, delta Greek letter, this triangle is a Greek letter, delta, represents change in.
Change in x here is one. We just increased x by one, what's gonna be our corresponding change in y? What's going to be our change in y? So let's see, when x is equal to one, we have two times one, plus three is going to be five.
So our change in y is going to be two. Let's do that again. Let's increase our x by one. Change in x is equal to one. So then if we're gonna increase by one, we're gonna go from x equals one to x equals two.
Well what's our corresponding change in y? Well when x is equal to two, two times two is four, plus three is seven. Well our change in y, our change in y is equal to two. Went from five- when x went from one to two, y went from five to seven. So for every one that we increase x, y is increasing by two.
So for this linear equation, our change in y over change in x is always going to be, our change in y is two when our change in x is one, or it's equal to two, or we could say that our slope is equal to two.
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