Which is The Graph of The Linear inequality 2x-3y 12

 So we have this inequality of two x plus three y less than or equal to twelve. And our aim is to graph it on this grid over here. And we want to highlight the region where all the coordinates x and obey this inequality. So it will be a highlighted region.

When we find our solution.  The first step to solving this problem is to actually graph the line two x plus three y equals twelve onto this grid. And then we'll determine which side we should highlight.  There are two ways to grab this line. One is to rearrange it into the form y equals MX plus b. Or we could just find a substitute for x and y values and get two points and connect those two. So I'll be using the y plus equals MX plus B method.

 So we have three y equals negative two x plus twelve. So y equals to third x plus four. So we know the y and seven because when x equals zero, the y coordinate is four.  So we put dot here and the.  The slope is negative two-thirds. So for example, once you go down two-thirds. So I would say when you go across three times, you go down in total two. I went out of the grid to emphasize that this will keep going forever in both directions.

  To determine which side we should highlight. We can check any point on either side. So I'll be just checking point here, and I'll be checking this point here, for example. But you could check any point as long as on either side. So if we check the coordinates.  X.  Equals one and y equals two, and the coordinates x equals three.  And y equals four, and we substitute.  This into the inequality, if it's untrue for one side, we don't highlight that side. If it's true for one side, we highlight that side. So I'll just demonstrate. 

Now if you substitute one-two, it.  Would be interstitial, it would be two times one plus three times two. And we check if this is less. Then or equal to twelve.  So it will be two plus six.   Is eight and eight is less than equal to twelve. So actually this site we found on our first call that this site is.  Okay, but for this example, I will.  Just test it to show you guys that this site should not be okay. 

So if we substitute this in quality, we have two times three plus three times four, that would be six plus twelve.  So this does not equal less than equal to twelve. So this side is wrong. The shaded part would look like this. Also, one more thing to note. You realize how this is less than or equal to inequality. It means that the line is also part of the solution.