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. And that makes sense.A lot of different ways that you could representĪ linear equation. And our slope is aĬoefficient on the x term, it is equal to zero. Like what we have over here and you might recognize that our y-intercept is negative seven, y-intercept is equal to negative seven. We could say, hey, this is the same thing as y is equal to zero times x minus seven. Slope or the y-intercept? Well, we could do a similar idea. Like what we had up here, how do we figure out the Let's say we had y isĮqual to negative seven, what's the slope and y-intercept there? Well, once again, you might say, hey, this doesn't look This as five x plus zero, and then it might jump out at you that our y-intercept is zero and our slope is aĬoefficient on the x term. I only have one term on the right-hand side What's the slope and y-intercept there? At first, you might say, hey, this looks nothing Let's say that we had theĮquation y is equal to five x. Here, what's the coefficient? Well, you can view negative x as the same thing as negative one x. But what's my slope? Well, the slope is theĬoefficient on the x term but all you see is a negative Might immediately recognize, okay, my constant term, when it's in this form, that's my b, that is my y-intercept. So, we could rewrite this as y is equal to negative x plus 12, negative x plus 12. Term before the constant term, so we might wanna do that over here. The standard form, slope intercept form, we're used to seeing the x Similar is going on here that we had over here. You can determine the slope and the y-intercept. Let's say that we have the equation y is equal to 12 minus x. And then it becomes a little bit clear that our slope is three, theĬoefficient on the x term, and our y-intercept is five, y-intercept. It doesn't matter which one comes first, you're just adding the two, so you can rewrite it as y isĮqual to three x plus five. So, if you wanna write it in the same form as we have up there, you can just swap theįive and the three x. Here, it's not five x, it's just five, and this isn't three, it's three x. Taken you a second or two to realize how this earlier equation is different than the one I just wrote. Y-intercept in this situation? Well, it might have Let's say if we hadįorm y is equal to five plus three x, what is the slope and the So, that's pretty straightforward but let's see a few slightly And b is just going to be thisĬonstant term, plus three. So, if we just look at this, m is going to be the coefficient Is equal to the slope, which people use the letter m for, the slope times x plus the y-intercept, which people use the letter b for. In slope intercept form where it has a form y Y-intercept in this example here? Well, we've already talked about that we can have something Let's say we have something of the form y is equal to five x plus three. So, let's start with something that we might already recognize. Like to do in this video is a few more examples recognizing the slope and
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