Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. The Cartesian coordinate system is made-up of two lines, the X axis and the Y axis. The X axis being the horizontal line, the Y axis being the vertical line. The two lines intersected a point called the origin, and the origin is written as 00. It's an ordered pair where the X comes first and the Y comes second. The X tells us how far left and right to go. the Y tells us how far up and down to go. Sometimes the X is called the abscissa, which is the domain or the input. The Y is sometimes called the ordinate or the range, which is the output. If our equations are not given in X&Y but perhaps in A&B, they're always then alphabetical order. The obsessa comes first, the ordinate comes second. So the A would be our domain and the B would be our range. So knowing all of that, we're going to graph a couple points -2 four that -2 tells us we're going to go 2 to the left, and the four tells us 4 up. So that's our point A. Point B, we're going to go 3 to the right and five up 12345. There's our point BC. We're going to go 0 to right or left, but down 1. So there's our Point C. Now when we look at these two axis, we can see that we're actually split up into what are called quadrants. The quadrant start in the upper right and that's quadrant one. And then quadrant 2 is the upper left three, the lower left for the lower right. If we thought about our ordered pairs in the quadrant one, we went to the right and we went up. So it would be a positive and a positive. Quadrant 2 we went left and then we went up. So negative, positive three, we went left and down, negative -4 we went right and down, positive, negative. So if we looked at our points AB and C, we could then talk about what quadrant each one is in. A is in quadrant 2B is in quadrant. 1C is actually not on a quadrant, but it's on the Y axis. Quadrants are usually used in Roman numerals, so I, I, I, I, I, or IV. Linear equations make a straight line going both directions. Nonlinear equations are things that aren't a straight line. So if we looked at Test points on a line, if Y equal to X -, 1, we're going to stick in the three for X and the 0 for Y and determine if it's a true statement or not. Does 0 equal 2 * 3 - 1? Does 0 equal 6 - 1? Does 0 equal 5? So the answer's no. So this point is not on the line. Point is not on the line. So if we thought about this graph, this line would actually look something like this. And so the .30 over here is not on that line. So let's look at this next point. This next point says the X is 0 and the Y is -1. So does -1 equal 2 * 0 - 1? Does -1 = 0 - 1 and the answer is yes. So the point is on the line. And if we look at this point zero -1 it's right here and it does indeed fall on the line. If we're given an example or we're given a problem where we want to actually fill in AT chart, typically we use a couple positive numbers, zero and a couple negatives. When we do AT chart, the more points we plot, the more accurate our graph will be. So this is saying what's our Y value when our X is two? 2 * 2 - 3 four -3 would give me one the next one. What's our Y when our X is 1? So 2 * 1 is 2 - 3 negative 1 the next one. What's Y when our X is 0, 2 * 0, zero -3 negative 3, the next one Y equal 2, * -1 -, 3, so -2 - 3, negative 5, and finally Y equal 2, * -2 - 3 or -7. So if we wanted to plot these points, we'd have two to the right and one up, one to the right and one down, 0 right or left, but three down, one to the left, five down, and two to the left, seven down. If we then connected these points, we could see that that would be a line that would keep going on and on. Examples of nonlinear lines would be things like Y equal X ^2. If we did AT chart, we would see that this would form what's called a parabola. Another one would be Y equal the absolute value of X. If we did AT chart here we would see that we get AV. Thank you and have a wonderful day.