Graph each inequality. 2x 3 - 4y

Question

Graph each inequality. 2x > 3 - 4y

Accepted Answer

Hello everybody. Everything. All right today that I'm going to be, look at this question that states draw the graph for the given inequality where the given inequality is X is greater than six minus five Y. Now, the first thing I'll note is that we have a greater than sign. This means that we have a strict inequality. So if you have a greater than sign or a less than sign, those are considered strict inequalities. If you have greater than, or equal to or less than or equal to, those are non strict inequalities for strict inequalities, you will have a dashed graph and I'll get more into that once we start graphing. But this is just something that you should know right away into the question. Now, when it comes to solving this inequality, I substitute the greater than sign with an equal sign. So if X is equal to six minus five Y and now I can just plug in points. So I know this is the shit, this is going to be the kind of a line equation because we have a Y and an X and such. So I'm going to plug in the intercepts. So at A Y equals zero, we'll have that X is equal to six minus five, multiplied by zero, which means that X is equal to six because five multiplied by zero is zero and six minus zero is zero or six or the 0.6 comma zero. So that would be the first point for our graph. Now, I can also try a point at X equals zero where we'll have zero is equal to six minus five Y. And then I can move the six over from the right hand side to the left hand side. So negative six is equal to negative five Y which will leave us with six divided by five is equal to Y or the 0.0 comma six divided by five. So now I have two points that I know I can connect with a line because we have our function is in the form of a line equation. So we can draw the Y axis and the X axis and we draw lines where we would mark as 12 and three, both on the Y axis or, or on the Y axis. And on the X axis, we know we go up to an X six. So we're draw lines at two, four and six. We'll label those on our X axis. And now we know that our Y intercept is zero, comma six divided by five, which means it's a little bit above one and our X intercept was six comma zero. So now I have two points that I can connect with my dash line. Remember this is where the strict inequality comes in. We will have a dash line. So we connect it using dashes and we extend that line to the left and to the right and it may come out a little bit curved because we're doing this handwritten, but it's supposed to be a straight line now because we have an inequality. We know that we're going to have to shade in a region since there won't be one single answer to an inequality and inequality will have multiple answers. So we're going to test the point in this case, I'll test zero comma zero or the origin and we'll see if that point is true or false for our inequality. So we plug in zero comma zero. We have zero as our X is greater than six minus five, multiplied by zero as our Y. And we'll have that zero is greater than six minus five multiplied by zero, which is six minus zero. And then we have zero is greater than six, which is false. So the origin won't be part of our graph. So the region that we have to shade in cannot include the origin. And to do that, we have to sit in the region above our graph because the origin is under a graph. So that's what we'll do. We'll shade in the region above our graph. And just like that, our graph is complete. We have a line with a negative slope with an X intercept at six comma zero and A Y intercept at zero, comma six divided by five with the line being connected by uh dashed dashes and the region above it being filled in. So I hope that was helpful. And until next time.

Graph each inequality. 2x > 3 - 4y

Key Concepts

Inequalities in Two Variables

Rearranging Inequalities into Slope-Intercept Form

Graphing the Boundary Line and Shading the Solution Region

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