Graph a Line in Slope-Intercept Form (Slope of -1) | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover how to graph a line in slope intercept form with a slope of -1. For our example, we have y = -x - 4. So, we need to figure out our slope and y intercept here. Now, we'll start with the slope. And this is where it's common for people to get held up because we just have ax. We don't see any slope, any number in front of it. Well, when we just see an x with no number written in front, there's an implied one in front of that x. In other words, it's understood that there's just one of that x. And in this case, we have a negative x. So this is actually -1x and we can even rewrite this with the -1 in front which we will do here in a second. So our slope is -1 and then our y intercept is -4. Now you may be thinking shouldn't we have + b plus the y intercept? Well, instead of writing + -4, so adding -4, the equation has been simplified. So, we don't have a double sign here, addition and then the negative. We can just write this as subtraction. Now, we do have the option of rewriting this with addition. That can help make the y intercept a little more clear. So, let's rewrite this as y = 1x + -4. So we included that -1 and then adding -4 and subtracting 4 give us the same thing. So either will work here. Again slope of -1 and y intercept of -4. Now for our slope, let's actually write this in fractional form. That way we can see our rise and run. And all we need to do here is put -1 over 1. So -1 over 1. And now we can clearly see that our rise is -1 and our run is pos1. Now let's graph. Starting with the y intercept, we need to plot a point at -4 on the y ais. So at 0 -4 which is right here. Now we need to go from that y intercept using our slope. So rise of -1 that means we need to go down one unit. And then our run is pos1 which means we go to the right one unit. So down one and then to the right one. Our second point is right here. Once we have those two points, we can draw our line through the points. And that's our line. And you'll notice since we have a negative slope here, the line is moving downward as it's moving from left to right. So there you have it. There's how to graph a line in slope intercept form with a slope of -1. I hope that helped. Thanks so much for watching. Until next time.