In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

Question

Accepted Answer

Hey everyone welcome back in this problem. We are asked to draw the graph of the given inequality in the rectangular coordinate system were given Y is greater than or equal to two. X plus four. Now, when it says rectangular coordinate system here, it just means our regular qwerty asian coordinate system, you can see in these graphs of the potential answers that the scale on the X and Y axis is the same. So this is just standard Cartesian coordinate system. Alright, so let's go down, give ourselves some room to work. We're gonna rewrite the inequality we were given so that we can see it and work with it. We have Y is greater than or equal to two, X plus four. Okay. Now what we're given in inequality and we want to graph it. What we want to do is start with graphing the equality. So we want to go ahead and graph y is equal to two, X plus four. Okay? And if we look at our inequality we have y greater than or equal to two X plus four. So this line Y equals two, X plus four is going to be included. Okay, Alright, so again Y equals two, X plus four. That's just a line. We know how to graph lines. Let's go ahead and find the X and y intercepts. That's going to help us draw that graph. Okay, so starting with the X intercept anyone, Y is zero. We get two X plus four. Okay, so we get x is equal to negative two and we have the point negative +20. All right. And then for our y intercept this is when X zero we get y is equal to four. And so we have the 40.4. Okay? We have a positive coefficient in front of the X. So we have positive slope. And so if we draw our graph here, X. Axis, why access? Alright. So Let's go ahead and draw in blue. Now we have our X intercept we have this point at -20. So that's going to be here. And then we have our y intercept the .04. It's gonna be here. Okay, we have a positive slope. So our line connects these two points like this. Alright. And this is the line Y equals two x plus four. Now, what we want to do, what we notice is that this line cuts the plane into two parts. The part kind of on the left? Above the line? Into the right or below the line. Okay, What we want to figure out is which part of this plane is included in our inequality? Well, our inequality is why is greater than or equal to two X plus four. Okay. So we want why values that are bigger than this line or equal to it. So we're going to take the part of the plane that's above the line. Okay, Because this is where the Y values are greater than outline. Now, another way we can figure out which part of the plane is included is to pick a particular point. Okay? So say we pick 00 if we pick the zero and we put it into our inequality, we're going to get zero is greater than or equal to four. Well, that's not true. zero is not greater than or equal to four. That means at that point is not part of our inequality or doesn't satisfy our inequality. And so the part of the plane that includes that point isn't going to be included. Okay, so that zero. This part below our line isn't included. Okay. Alright. So that's our graph. Let's go back up to our answer choices. Now we know we're including the left part. Okay? So we have either answer choice A or B. Now we need to pay attention to those intercepts. Okay? And we see that we have the graph of A. Because we had the X. Intercept at negative two and the Y intercept at four. Okay, So our answer here is going to be a thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

Key Concepts

Linear Inequalities

Graphing Linear Equations

Shading the Solution Region

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