Hello, wonderful mathematics people. This is Anna Cox from Kellogg Community College. Linear inequality. We're going to graph a line and they're going to look at whether the line should be solid or dotted based on the inequality, and we're going to shade it. So when we graph a linear inequality, if it's greater than or less than, it's not equaling the line. So we're going to have it be a dotted line in these case. In these cases, if it's greater than or equal to, less than or equal to, it's going to be a solid line. Now, if it's greater than or greater than or equal to, if we have it in Y equal MX plus B form, to start, we're going to have above the line shaded. If it's less than or less than or equal to, once again, if it's in Y equal MX plus B form, it's going to be below the line. So if we look at Y greater than two X -, 3, we're going to go up or we're going to go to the Y intercept of zero -3 Remember, Y intercepts the number at the end. So we're going to go down 3. Our slope here is 2, and we could think of that as 2 / 1 rise over the run. So we're going to go up two and to the right one, up two to the right one, up two, to the right one. And this, because it's just greater than is going to be a dotted line. And if it's greater than, I need to shade above the line. So that's my final solution for that first example. If I have Y less than or equal to three halves X + 1, my intercept is 01 and now my slope is 3 halves, so I'm going to go up three and to the right two. I could also think of that as down 3 and to the left 2. Because we know a negative divided by a negative is really a positive, it's less than or equal to, so it's going to be a solid line this time. And because it's less than, we're shading below the line Y greater than 5 halves. Well, remember, if Y equals some constant, this is just a horizontal line. So when we look at Y greater than 5 halves, 5 halves is 2 1/2. So we're going to put in a dotted because it was just greater than at 5 halves, and then we're going to shade above. If it had been greater than or equal to, we would have done a solid X being a relationship with some constant, is a vertical line. So if we go to the vertical line, X equal 1/2, and I might scale this. Let's scale this by 1/4. So if I scale this by 1/4, this first one's 1/4, the next one would be 1/2, and it's going to be a dotted because it was just less than. And then I'm going to shade it to the left just like in a number line, if it's a vertical, if it's X less than, we're left. And if it was X right greater than we're right. The next example after you do your try it, we're going to actually put this one in Y equal form. So -3 Y less than or equal to negative two X + 6 when I divide by a negative. Remember we're going to flip the inequality side, so we're going to get Y greater than or equal to 2 thirds X -, 2 Y intercept zero -2 slope 2/3. So zero -2 slope up two into the right three, up two to the right three, or down to into the left three. It's going to be a solid line because it was greater than or equal to, and if it's greater than or equal to, we're going to shade above. Now, one way you could check it is to choose any point, and we usually choose the origin just because it's easy. If I choose the origin and stick it into the original equation, I should come up with a true statement if it's shaded. So 2 times zero, 0 - 3 * 0. So is 0 less than or equal to six? And the answer is yes. So I know that at the origin it should be shaded. If this had come up as a true statement, I would know that the origin wasn't in the shaded area and I would shade the opposite area. And the last one's for you to try. Thank you and have a wonderful day.