In Exercises 1–26, graph each inequality. y−3

Question

In Exercises 1–26, graph each inequality. y>−3

Accepted Answer

Hey everyone in this problem. We are asked to graph the following inequality and were given why greater than -10. Now, the first thing we want to do when we have an inequality like that, let's just give ourselves some more room to work, Is to graph the equality. So we're given why is greater than -10? We want to go ahead and graph the inequality or sorry, the equality why is equal to negative 10. This is going to create a boundary, it's going to separate the plane into two pieces and then we can figure out what side of that boundary we should be including in our inequality in which one is excluded. So we have y equals negative 10 is going to be our boundary. And if we go ahead and graph that really choose And we're gonna say that each of these is -2. So this point is going to be negative 10. And so the line y equals negative 10 is going to be a horizontal line at that y value of -10. The question is do we draw it as a solid line which indicates that we're including the value Y equals negative 10. Or do we draw it as a dashed or dotted line? Which indicates that we're not including the value of y is equal to negative 10. Now, in this case our inequality is why greater than negative 10. Okay, there's no greater than or equal to So we don't actually want to include negative 10. So we're going to draw this as a dashed line. So we draw this as a dash line and this is a line. Y is equal to negative 10. Now the question is is above this line included in our inequality or is below this line included in our inequality? Well, we want why to be bigger than negative tent. Okay. Where do we have larger Y values? Well as we go up the y axis we get larger and larger Y values. So we want to be above this line. So we want to take everything above this line to be included in our inequality. All right. Now, if you didn't see that or you were having a hard time figuring out which side of that line we should be on whether we're including everything above that line or below that line. You can always test the point. Okay? So if you take the point se Y equals zero. Okay, So X zero, Y zero. Then you're going to have zero which you know is greater than negative 10. So that satisfies the inequality which means at that point is included. So you can always test the point to see. And if you were to take a point below it wouldn't satisfy the inequality. So you would know that that point is not included. Alright, So let's go look at our answer choices. Now A and B. We can already eliminate because those are vertical lines and we know that our boundary Y equals negative 10 is a horizontal line. So we're looking at a horizontal line. So we're looking at Crd and we know that we're including everything above our line Y equals negative 10. So we have option C as the answer. That's it for this one. Thanks everyone for watching. See you in the next video.

In Exercises 1–26, graph each inequality. y>−3

Key Concepts

Graphing Linear Inequalities

Boundary Lines and Their Types

Coordinate Plane and Regions

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