In Exercises 1–26, graph each inequality. y2x−1

Question

In Exercises 1–26, graph each inequality. y>2x−1

Accepted Answer

Hey everyone welcome back in this problem. We are asked to grab the following inequality and were given Y is greater than six X -3. Let's go down to the bottom of our page. Just give ourselves some more room to work And we have Y is greater than six X -3 is what we were given in the problem. Now, the first thing we want to do when we're given in inequality and we're asked to graph it is actually graph the equality. So we want to switch this inequality symbol which with an equal sign And we want to look at this so we have y is equal to six X -3. And this is going to give us the boundary of our inequality. Okay, that's going to divide the plane up into two portions and then we can figure out what portion of the plane is included in our inequality, in which portion isn't. So we recognize this as the equation of a line, right? We have Y equals mx plus B. And this is gonna be a line with slope. Okay, when we're looking at a line in this format Y equals mx plus B. The coefficient in front of the X term is going to be our slope. So we have a line with slope six, let's go ahead and find the X intercept in the Y intercept. Because that's going to help us graph it. So if we're looking for the X intercept This is when Y is equal to zero And so we get zero is equal to six, X -3. Six. X is equal to three. And so we get X is equal to one half doing the same for the Y intercept the Y intercept is going to be one, X. Is equal to zero. And so we get Y is equal to negative three. Alright, so our X intercept X equals one half, gives us the 10.1 half zero. And our Y intercept Y equals negative three, gives us the 30.0 negative three. So if we go ahead and graph this line We have the .120. She's going to be here. Okay for our X intercept And we have the zero and -3 which is gonna be down here for our Y intercept. Now the question is do we draw this line as a solid line indicating that we're including that boundary in our inequality or do we draw it as a dot or dash line indicating that we're not including it? Well our problem gives us Y is greater than six x minus three. It doesn't give us Y is greater than or equal to six x minus three. So we don't want to include the boundary. So we're going to draw it as a dashed line. Okay, So we're going to connect these two points To create our line and it's gonna look something like this. Okay, so this is our line, y equals six X -3. Now like I said this divides the plane into two portions and we need to figure out what side we include. Well we want why to be greater than this line. We're looking at why values cara y values are increasing as we go up this Y axis and so we want to be above this line. Okay, So everything above this line which is kind of above and to the left of this line is going to be included in our inequality. Everything below it to the right isn't. Okay. Now, if that's confusing to her or if you get stuck on that, what you can do is you can always test particular points. So if we were to test the point say 00. Okay well on the left hand side of the inequality we would have zero and on the right hand side we would get zero minus three. So we have negative three. So we get zero is greater than negative three. That's a true statement. That means that that point satisfies our inequality. So it's included. Ok, so that 30.0.0 which we know is kind of to the left of that line is included. So we know that that's the side that were included and you can do the same thing. You could test a point on the right. It wouldn't satisfy the inequality. So you know that we're not including those points. Alright, so let's go back up to our answer choices. Now that we have our drawing debt and choose the one that matches what we've just drawn. So we have a line with slope six. Okay, that's a positive slope. So we know we're looking at option a or B. We found the X intercept is one, half the Y intercept is negative three. And so both of these lines look like they have those values, and it's just a matter of what side of that line we include. So we're going to include everything above to the left of that line and exclude everything to the right. So we have option A. Thanks everyone for watching. I hope this video helped you in the next one.

In Exercises 1–26, graph each inequality. y>2x−1

Key Concepts

Inequalities

Graphing Linear Equations

Shading Regions in Graphs

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