 This video is called Introduction to 3.3. Hopefully you're watching this video first before you watch the others that follow in tonight's homework. Today's or tonight's lesson is all about the word slope. You're gonna get very used to hearing about slope and hopefully very comfortable with what it means and how you can find it. Usually when I ask students, when they hear the word slope, what do they think of? I hear a lot of different responses and I'll go over a few of them now. The most wordy response, the definition of slope, I always like to think of it as being the steepness of a line. Lots of students, when they hear slope, will tell me y equals mx plus b, which isn't a bad thing to think of. This is actually an equation of a straight line in slope intercept form where the m represents your slope. So in a math equation in slope intercept form, this m would get replaced with a number that represents slope. So notice or remember that slope is the number right in front of the x and it's multiplying the x when you're in slope intercept form. Lots of students say slope, it's usually a fraction and lots of times it is where the numerator tells you how far up or down and the denominator tells you how far to the left or right a line goes between two points on a line. The official formula to help you find slope is y2 minus y1 over x2 minus x1. That formula you will use a lot if we ask you to calculate the slope of a line because all you need are two points on that line and you can plug them into this formula and you'll find your answer. You will have a chance to practice this in later videos. When something had a line has a positive slope, you know it's positive because from left to right, the line goes up and your slope will be a positive number. If a line has a negative slope, you can tell just by looking at it because from left to right, the line will go down. Maybe it'll go down very steeply and sharply or maybe it'll be more gradual but from left to right, it goes down. You can remember that the number will then be negative. A slope of zero is when you have a straight horizontal line and undefined slope is when you have a vertical one. I always remember the two being that when you have a slope of zero, think of it like skiing. You can ski on a hill with a positive slope. You can ski on a hill with negative slope and you'll have a good time. Can you ski on the ground that has a slope of zero? You sure could but it might be a little bit harder and you might hope that you have cross-country skis. So a positive slope, a negative slope, and a slope of zero, if you think of these lines as hills, you could ski on all of them, downhill, downhill, cross-country. Where a vertical line that has an undefined slope, you can't go skiing on a vertical line. It's a cliff, you would just fall right off of it and bad things would happen to you. So keep in mind, positive slope, negative slope, slope of zero are things you can ski on. The undefined slope is the one that's the vertical line. You cannot ski on it, you would get hurt. So that's just kind of a silly way to help remember the difference between slope of zero being horizontal and undefined being vertical.