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. In x, delta Greek letter, this triangle is a Greek letter, delta, represents change in. One, so we could write that our delta x, our change So let's plot some more points here and I'm just gonna keep And if you made that conclusion, you would be correct! And we're about to see Now you might be saying, well it says slope-intercept form, it must also be easy to figure out the slope from this form. So it's very easy toįigure out the intercept, the y-intercept from this form. When x is equal to zero and y is equal to three, it's gonna be this point right over here. The y-intercept here is going to happen when it's written in this form, it's going to happen The reason why this is called slope-intercept form is it's very easy to calculate the y-intercept. Through it and this line contains this point, this is When x is equal to zero and y equals three, this is, we're right on the y axis. Here, zero comma three, this is x is zero, y is three. 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 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 That is my x axis and let me mark off some hash marks here, 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. You're only left with this term right over here, y is equal to three. Two times zero is zero, that term goes away, and Gonna pick some x values where it's easy to calculate the y values. I'm gonna try to graph it, I'm just gonna plot some points here, so x comma y, and I'm To you, let's just try to graph this thing. And hopefully in a few minutes, it will be obvious why itĬalled slop-intercept form. Here is often called slope-intercept form. 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 Very useful representation of a linear equation and 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 You can get from one to the other with logicalĪlgebraic operations. This equation here or that equation up on top. You could actually simplify this and you could get either Ways where I get it to, and I'm gonna do it right now, but this is another way of 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. Had the linear equation y is equal to 2x plus three, that's one way to represent it, but I could represent this inĪn infinite number of ways. A lot of different ways that you could representĪ linear equation.
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