Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. Graphing linear inequalities. We're going to graph linear inequalities just like we graph a line. The difference is now we're going to do shading. If we have greater than or less than, we're going to use dotted lines or dashed lines. If we have greater than or equal to, less than or equal to, we're going to use solid lines. So we're going to take an example Y greater than two X -, 3. Our Y intercept is the .0 negative 3 and our slope is 2 / 1. So zero -3 up to and over one up 2 / 1 up 2 / 1 up 2 / 1. I could also go down to and back one. It was just greater than. So we're going to put in a dotted line. It wasn't or equal to. Now we need to figure out where we're going to shade, and we're going to shade greater than the line. Greater than the line would be above the line, so we're going to shade up here. If we're not certain as to where we shade, we can choose a point. Usually choosing the origin is easy. So if I choose the .00, I'm going to actually put it into the equation, and if it's a true statement, I know that's the side that I should shade. So is 0 greater than 2 * 0 -, 3? Is 0 greater than -3? This is a true statement. So shade the side that has the .00. Let's look at some other examples. Y less than or equal to three halves X + 1. Our Y intercept is the .01. Our slope is 3 halves, so if we go to 01 now, we're going to go up three and to the right two. Or I could go down 3 and to the left two, down 3 and to the left two. This time it's going to be a solid line because it was or equal to. I want Y less than or equal to. If I want less than the line, I want below the line. So we're going to shade down here. If we wanted to do a test point, we could choose any point we want any any point. Let's choose a point that's not going to work just to show it. So let's do the point -3 two. If I stick a -3 two, I'm going to get 2 less than or equal to three halves. Times -3 + 1 is 2 less than or equal to three halves times -3 that -3 is understood to be over a 1 so -9 halves plus one is 2 less than or equal to -7 halves. No, that's not true. So it tells me don't shade in this area if we wanted to try the origin again. So the .00 is 0 less than or equal to three halves. Times 0 + 1 zero is less than or equal to 1, so it's true. So shade this side doing a few more examples. Y greater than 5 halves. Well, Y equal 5 halves is a horizontal line, so if I want Y greater than 5 halves, it's going to be dotted, and we want greater than greater than it's going to be above, so we're going to shade above. How about if it was an X line? X less than 1/2 X is a vertical line, so X less than 1/2, it's going to be dotted because it wasn't or equal to. And if we think about this being similar to a number, line less than is to the left, so we're going to shade to the left. Now what if the X&Y are on the same side? We need to solve it and put it in slope intercept form. So in this example, we're going to subtract our two to the other side, and then we're going to divide by a negative, remembering to flip the inequality sign when we divide by a negative. So Y is going to be greater than or equal to 2/3. XI lost my X -, 2, so my Y intercept is the .0 negative 2, and my slope is 2/3, so zero -2 slope 2/3 up 2 / 3 up 2 / 3 down to back 3. It's going to be a solid line this time because it was or equal to, and I want greater than or equal to the line. I always want to use it when it's all solved. So Y greater than or equal to. So now we're going to shade a buff. Thank you and have a wonderful day.