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# Slope and y-intercept from equation

## Video transcript

- [Instructor] What I'd like to do in this video is a few more examples recognizing the slope and y-intercept given an equation. So, let's start with something that we might already recognize. Let's say we have something of the form y is equal to five x plus three. What is the slope and the y-intercept in this example here? Well, we've already talked about that we can have something in slope intercept form where it has a form y 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. So, if we just look at this, m is going to be the coefficient on x right over there. So, m is equal to five. That is the slope. And b is just going to be this constant term, plus three. So, b is equal to three. So, this is your y-intercept. So, that's pretty straightforward but let's see a few slightly more involved examples. Let's say if we had form y is equal to five plus three x, what is the slope and the y-intercept in this situation? Well, it might have taken you a second or two to realize how this earlier equation is different than the one I just wrote. Here, it's not five x, it's just five, and this isn't three, it's three x. So, if you wanna write it in the same form as we have up there, you can just swap the five and the three x. It doesn't matter which one comes first, you're just adding the two, so you can rewrite it as y is equal to three x plus five. And then it becomes a little bit clear that our slope is three, the coefficient on the x term, and our y-intercept is five, y-intercept. Let's do another example. Let's say that we have the equation y is equal to 12 minus x. Pause this video and see if you can determine the slope and the y-intercept. All right, so, something similar is going on here that we had over here. The standard form, slope intercept form, we're used to seeing the x term before the constant term, so we might wanna do that over here. So, we could rewrite this as y is equal to negative x plus 12, negative x plus 12. And so, from this, you might immediately recognize, okay, my constant term, when it's in this form, that's my b, that is my y-intercept. So, that's my y-intercept right over there. But what's my slope? Well, the slope is the coefficient on the x term but all you see is a negative here, what's the coefficient? Well, you can view negative x as the same thing as negative one x. So, your slope here is going to be negative one. Let's do another example. Let's say that we had the equation y is equal to five x. What's the slope and y-intercept there? At first, you might say, hey, this looks nothing like what we have up here. I only have one term on the right-hand side of the equality sign. Here, I have two. But you could just view this as five x plus zero, and then it might jump out at you that our y-intercept is zero and our slope is a coefficient on the x term. It is equal to five. Let's do one more example. Let's say we had y is equal to negative seven, what's the slope and y-intercept there? Well, once again, you might say, hey, this doesn't look like what we had up here, how do we figure out the slope or the y-intercept? Well, we could do a similar idea. We could say, hey, this is the same thing as y is equal to zero times x minus seven. And so now, it looks just like what we have over here and you might recognize that our y-intercept is negative seven, y-intercept is equal to negative seven. And our slope is a coefficient on the x term, it is equal to zero. And that makes sense. For a given change in x, you would expect zero change in y 'cause y is always negative seven in this situation.