Algebra (all content)
- Intro to graphing two-variable inequalities
- Graphing two-variable inequalities
- Graphs of inequalities
- Two-variable inequalities from their graphs
- Two-variable inequalities from their graphs
- Intro to graphing systems of inequalities
- Graphing systems of inequalities
- Graphing two-variable inequalities (old)
- Systems of inequalities graphs
- Graphing inequalities (x-y plane) review
Graphing two-variable inequalities (old)
An old video where Sal graphs the inequality y-4x<-3. Created by Sal Khan and Monterey Institute for Technology and Education.
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- I dont get the whole concept on inequalities and the filled dot and unfilled dot if anyone could answer my question it would be really helpful(10 votes)
- The closed dot is on an equal to, it is including that point. An unfilled dot is in an less than or equal to, it is not including it.(9 votes)
- At1:38what is a boundry?(7 votes)
- A boundary is the collection of all points of a given set having the property that every neighborhood of each point contains points in the set and in the complement of the set.(5 votes)
- I really don't get the concept of with the < and > and I have HW on this and I am really confused which half should I shade in. Help please(2 votes)
- Basically, if y > 2x+3, you graph:
y = 2x + 3
Then, you have to decide 2 things:
1) dotted line or solid line
If the sign is < or >, use dotted line
if the sign is <= or >=, use solid line
2) Shade above or below
if y>something or y >= something, shade above
if y<something or y <= something, shade below(6 votes)
- At4:36do you need a boundry line?(6 votes)
- No because that point was just an example in the shaded region to support the equation.(0 votes)
- how do u graph multiple inequalities(3 votes)
- See the https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-through-examples video & exercise series for dealing with that.(1 vote)
- How do yo know to shade to the left or to the right? If it's less than wouldn't it be to shaded to the left?(1 vote)
If it is less than, shade below. If it is more then shade above.
If you think of it as left and right, then the answer changes when the slope is positive or negative. This makes using left and right much harder to remember.
It is best to think of "less than" as below and "greater than" as above.
The is one exception: If it is a vertical line such as x<1 then there is no above or below. If the line is vertical, you would shade "less than" to the left and "greater than" to the right.
I hope that helps.(5 votes)
- So, do you ever need to solve the inequality before graphing it? Or, do you just graph it anyway like you did in the video?(3 votes)
- Great question. You should always be able to graph it as an inequality. You really can solve it before graphing, but that is up to you most of the time. Make sure that what you do is what the question asks you to do. I hope this helps!(1 vote)
- no the "y" value doesnt change unless you are dividing or multiplying by negatives hope i helped :)(3 votes)
- Ok, I can draw the boundary line and I understand the difference between dotted and solid boundary lines. But how do i know which side to shade? Please be detailed and thanks in advance.(2 votes)
- Where would you use this(2 votes)
- Some jobs like nurses, management people, professors, mostly people who have computers as their jobs, etc have to know what linear inequalities are.(2 votes)
Graph the inequality y minus 4x is less than negative 3. So the first thing we could do is we could kind of put this in mx plus b form, or slope-intercept form, but as an inequality. So we're starting with y minus 4x is less than negative 3. We can add 4x to both sides of this inequality. So let's add 4x to both sides of this inequality, and then we'll just have a y on the left-hand side. These guys cancel out. So you have y is less than 4x minus 3. We could have had negative 3 plus 4x, but we want to write the 4x first just because that's a form that we're more familiar with. So it's less than 4x minus 3. And now we can attempt to graph it. But before I graph it, I want to be a little bit careful here. So let me draw our axes. So this is the x-axis, and is that is the y-axis. And we want to be careful, because this says y is less than 4x minus 3, not less than or equal to 4x minus 3, or not y is equal to 4x minus 3. So what we want to do is kind of create a boundary at y is equal to 4x minus 3, and the solution to this inequality will be all of the area below that, all of the y values less than that. So let's try to do it. So the boundary line would look like-- so let me write it over here-- so we have a boundary at y is equal to 4x minus 3. Notice this isn't part of the solution. This isn't less than or equal. It's just less than. But this will at least help us draw, essentially, the boundary. So we could do it two ways. If you know slope and y-intercept, you know that 4 is our slope and that negative 3 is our y-intercept. Or you can literally just take two points, and that'll help you define a line here. So you could say, well, when x is equal to 0, what is y? You get 4 times 0 minus 3, you get y is equal to negative 3. And we knew that because it was the y-intercept. So you have 0, and then you have 1, 2, 0, and negative 3. And then you have the point, let's say, when x is equal to-- I don't know-- let's say when x is equal to 2. When x is equal to 2, what is y? We have 4 times 2 is 8 minus 3, y is then going to be equal to 5. So then you go 1, 2, and you go 1, 2, 3, 4, 5. And so you have that point there as well. And then we can just connect the dots. Or you could say, look, there's a slope of 4. So every time we move over 1, every time we move 1 in the x direction, we move up 4 in the y direction. So we could draw it like that. So the line will look something like this. And I'm just going to draw it in a dotted line because, remember, this isn't part of the solution. Actually, let me draw it a little bit neater because that point should be right about there, and this point should be right about there. And then this boundary line I'm going to draw as a dotted line. So it's going to look something like that. I draw it a dotted line to show that it's not part of the solution. Our solution has the y's less than that. So for any x, so you pick an x here, if you took 4x minus 3, you're going to end up on the line. But we don't want the y's that are equal to that line. We want for that particular x, the y's that are less than the line. So it's going to be all of this area over here. We're less than the line, and we're not including the line, and that's why I put a dotted line here. You can also try values out. You can say, well, this line is dividing our coordinate axes into, essentially, the region above it and the region below it, and you can test it out. Let's take something that's above it. Let's take the point 0, 0 and see if that satisfies our inequality. If we have y is 0 is less than 0 minus 3, or we get 0 is less than negative 3. This is definitely not the case. This is not true. And it makes sense because that 0, 0 is not part of the solution. Now, we could go on the other side of our boundary line. And we could take the point, I don't know, let's take the point 3 comma 0. So let's say that this is the point-- well, that's right. There's a point 2 comma 0. Let's take the point 3 comma 0 right over here. This should work because it's in the region less than. But let's verify it for ourselves. So we have y is 0. 0 is less than 4 times 3 minus 3. 0 is less than 12 minus 3. 0 Is less than 9, which is definitely true. So that point does satisfy the inequality. So in general, you want to kind of look at this as an equal to draw the boundary line. We did it. But we drew it as a dotted line because we don't want to include it because this isn't less than or equal to. It's just less than. And then our solution to the inequality will be the region below it, all the y's less than the line for x minus 3.