In Exercises 1–26, graph each inequality. x−2y10

Question

In Exercises 1–26, graph each inequality. x−2y>10

Accepted Answer

Hey everyone welcome back in this problem. We have to graph the following inequality were given X -4, Y is greater than 16. We're gonna go to the bottom here so we have some room to work, We're going to rewrite that inequality we were given and were given X -4, Y is greater than 16. Now in this inequality we have an X term degree, won a wide term to do the degree one K. The exponents on both of those are just one. And then we have a constant term. When we have an inequality like this, sometimes it's easier to write it in a familiar form. Okay. And we know that Y equals mx plus B. Is kind of the familiar way to write the equation of a line. We have a white term, an X term in this constant term. So let's try to rearrange this inequality so that it's written kind of like a line. So if we move this negative four Y to the right hand side and the 16th to the left hand side, we're going to have x minus 16 is greater than four Y. And then we're going to divide by four and we're just gonna write this the other way. So we have Y is less than X over four minus 16/4, which is four. So now we have why is less than X over 4 -4. Okay, this is the same inequality. We've just rewritten it to look more like the equation of the line. Now when we have inequality and we want to graph it. The first thing we want to do is to graph the equality. So we want to change that inequality to an equal sign. So we have y is equal to X over 4 -4. We're going to graph this line first. That's going to break up the plane into two portions and then we can figure out afterwards which side of the plane we're going to include in our inequality. Now we have this line here and again. It's in this format Y equals mx plus B. We know that M is the slope. So our slope is going to be 1/4. Now let's find your X. And Y intercepts. That's just gonna help us graph this is going to give us two points and then we can graph our line. So if we're looking at the X intercept this is going to be when y is equal to zero. Now when y is equal to zero we have zero is equal to x minus four. Sorry, X over four minus four. This tells us that X over four is equal to four. And if we multiply up we get that X is equal to 16. Okay? So we have our X intercept at X equals 16. We have the .160. And if we do the same with the Y intercept, okay, this is gonna be when X is equal to zero. Well we find that y is going to be equal to negative for We plug in zero here we just get -4. And so we have a zero and negative four so we have two points. We know the slope, we can go ahead and draw this line. So let's do that. Alright, so we have the point 16 and zero. So we're gonna draw that way over here. 16 and zero And we have the 0.-40. That's gonna be about here. Sorry zero negative four, negative 400 negative four. X value zero, Y value negative four. Now, what we need to figure out is when we draw this line, do we draw it as a solid line indicating that we include that line in our inequality or do we draw it as a dotted or dashed line? Meaning that we're excluding it from our inequality? Well, in our problem we are given when we rearrange why is less than X over four minus four? Okay. We don't have less than or equal to, we can't be equal to this line that's not included. So we're gonna draw it as a dashed line because we don't include the equality. So we draw this dash line like this And that is our line, y equals x over 4 -4. Now when we go to figure out what side of the line to be on this is we're writing it in this form, why less than X over 4 -4. Kind of comes in handy. What we see here is we want Y values that are less than this line. Where do we have Y. Values less than well if the y value is less than that means it's below the line. Okay. Because the further down we go the more negative or the less or why values get Okay. So we want to include below this line. Now if you are stuck figuring out which which side of the line or that is confusing for you to do it that way but you can do is choose the point. So say you choose the 0.0.0. Okay, choose the 0.0. And you plug this into the equation on the left hand side, you're going to get zero and on the right hand side you have negative four. So you end up with the inequality zero is less than negative four. That's not true. Zero is not less than negative four. That's not true. So what that tells us is that 40.0 is not included in our inequality. So above the line where we have that 0.0 is not going to be shaded in. Okay, so that just helps you pick what side of the plane you are shading in. So let's go back up to our answer choices now that we've drawn our graph and see which one kind of matches our sketch. So we found that we weren't going to be including the line. The line was going to be a dashed line. Okay, So we can already eliminate C. And D. Because those have solid lines. Now, we have this line that we've drawn the line X over 4 -4, and we found that we wanted to include the part below that line, so that matches with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–26, graph each inequality. x−2y>10

Key Concepts

Graphing Linear Inequalities

Converting Inequalities to Slope-Intercept Form

Testing Points to Determine the Solution Region

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