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Hi, this is Julie Harland and I'm your math gal.
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Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic.
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This is part 5 of graphing linear inequalities into variables.
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And on this video we're going to graph these two inequalities.
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Alright, before I do them, put the video on pause and see if you can do this one all on your own.
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3x minus 2y is less than or equal to 6.
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Alright, step 1.
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Step 1 is always to graph it as if it's an equation here, right?
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So the line, so we're going to graph 3x minus 2y equals 6.
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And we have to decide whether we're going to have a solid line or a dotted line.
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Solid line means it's part of the solution.
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And so since it's got an equal sign here, this is part of the solution.
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So use a solid line since it's part of the solution.
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Alright, now it's up to you how to graph that.
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I like using the x and y to set method.
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I think, well, if I put in 0 for x, what would y be?
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So when I put in 0 for x, y is going to be negative 3.
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So 0 for x, y, negative 3, I know that's going to be one order pair on this line.
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And then I'm going to put in 0 for y.
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If I put in 0 for y, I get 3x equals 6, so x will be 2.
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But you can use any method you want.
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You can solve for y and put it in slope intercept form.
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And so if you did put it this in slope intercept form,
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just going to remind you how to do that quickly.
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Negative 2y is equal to negative 3x plus 6,
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and divide by negative 2.
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You would have y equals 3x minus 3.
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And notice this tells you that the y intercept is negative 3.
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And the slope is 3, have I go over 2 and up 3?
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I get the same two points.
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And then we graph our line.
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So I'm using a solid line because of the equation.
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So it doesn't matter the method you use.
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Sorry, my line doesn't look very straight here.
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I'm free drawing it.
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But step one is to simply graph that line and use the solid line.
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Now we have to decide which side to shade.
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So which side are we going to shade?
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Well, I pick a point off the line.
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And if I can, I always choose 0, 0.
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So I'm going to check 0, 0.
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And the original inequality.
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And I'm only just going to use the less than symbol.
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Because we're trying to do that.
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Oops, that's supposed to be a 2.
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Alright, so I'm going to put in 2 for x and 2 for y.
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And hopefully you can see what happens when I put in 2 for x
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and 2 for y.
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I'm going to get 0 minus 0.
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0 is less than 6.
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And is that true?
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So that means 0, 0 is a solution.
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A solution, just one of them.
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So I'm going to shade that side.
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Where's 0, 0 is?
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There we go.
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Now, what if I had taken this original equation?
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3x minus 2y is less than or equal to 6.
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And tried to solve for y.
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Be careful here.
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First, just subtract 3x from both sides.
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And I'm not sure that's all going to show up here.
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So let's skew it over a little.
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And, back to I didn't move it over enough.
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There we go.
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And then when I divide by negative 2, be careful here.
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What happens when you divide by a negative?
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This is still less than or equal.
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When you divide by a negative, that switches to greater than or equal.
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So be careful.
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So I get y is greater than or equal to 3x minus 3.
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And the reason I'm showing you this is because notice,
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if you had solved for y carefully, you shade above the line,
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because it says y is greater than or equal.
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It's x.
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But in any case, it's always good to check a solution anyway.
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So you don't need to do this.
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Just sort of showing that it all kind of matches and makes sense if you do it.
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All right, let's go on to this problem.
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x plus 3y is less than negative 3.
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Try it on your own first.
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Put the video on pause.
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Get out some graph paper.
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Pay attention to whether you need a solid line or a dotted line.
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Checkpoints, do your shading, et cetera.
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All right, we'll our first step be.
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Our first step will just be graph x plus 3y equals negative 3.
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Now remember, it doesn't matter what method you used to graph a line.
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You just have to get the correct line.
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And am I going to use a solid line or a dotted line?
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Is this part of the solution that line?
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That's the big question.
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No, it's not, because notice there's no equal sign up here.
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So we have to use a dotted line since it's not a part of the solution.
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All right, so did you graph your line?
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All right, I graphed my line and I know it's not really straight, but I can't use a ruler on my video.
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But you should use a ruler or something to make your dotted line look straight on your paper.
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So here it is.
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And you could have done that.
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And you could have done this by solving for y and putting it in slope intercept form.
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In fact, we could actually take the original inequality and easily solved by subtracting x from both sides.
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And I'm going to write that as negative 1x minus 3.
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And then dividing by 3.
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Now, I'm dividing by a positive number, so remember if I divide by a positive number, I don't have to switch the inequality sign.
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So y is less than negative x.
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I'm sorry.
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Negative 1 third x minus 1.
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And that's the line I have over here.
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The slope intercept form gives me the intercept of negative 1.
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And I have a slope of negative 1 third.
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But I actually did it by using the x and y intercept method.
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I plugged in 0 for y to find out x was negative 3, which is right here.
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And then I put in 0 for x to get y was negative 1 right here.
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In any case, you hopefully have a straighter line to meet.
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So the next thing is to pick a point, not on the line.
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So I'm going to choose 0, 0.
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Because that's the easiest one to plug into the original.
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And always plug it into the original, not this, because you might have made a mistake here.
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So always plug it into the original.
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So we're going to put in 0 for x and 0 for y, which gives you 0 plus 0.
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And is that true or false?
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Is 0 less than negative 3?
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Nope.
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False.
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So that's not part of solution.
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Right?
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So I do not want to shade that part of the line.
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I want to do not want to shade the part of the line where 0, 0 is.
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I want to shade the other side of the line.
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Now, if you look when we did solve it, I have y is less than negative 1 third x minus 1.
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Remember when you just have y on one side, and you have less than, it should be shaded below the dotted line.
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So it matches up there as well.
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And there you have it.
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In these five videos, we've done a lot of different inequalities,
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graphing inequalities with two variables.
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So just keep practicing.
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Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.