Main content

### Course: Algebra (all content) > Unit 2

Lesson 14: One-step inequalities# Solving and graphing linear inequalities

How to graph on a number line and coordinate plane. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- when sal shows that no matter what x is, y is always going to be greater than 5, how can you tell why he knows :?(3 votes)
- Colby,

The equation y>5 is a linear inequality equation.

Let's first talk about the linear equation, y=5

If you wrote the linear equation in the form of y=Ax+B, the equation would be

y=0x + 5.

When x=1, what is y? y=5

And when x = 2, what is y? y=5

So no matter what x is, y=5

So whatever we put in for x, we get x*0 which always = 0. So for whatever x we use, y always equals 5.

The same thing is true for y>5.

It could be rewritten as

y > 0x + 5.

And again, no matter what x we use, y is always greater than 5.

I hope something I said here helps it click for you.(53 votes)

- what happens if you have an equation like " 4x < 32" ? How do you answer it and graph it?(13 votes)
- The y-value will be infinite, so just raw a vertical line crossing the point (4,0) and shade away from zero. This way , ANY y-value can work.(9 votes)

- At1:39what does Sal mean by this?(6 votes)
- He means that Y isn't equal to 5, but is greater than 5. Therefore, you wouldn't include 5.(5 votes)

- y=-5x+3 i dont know how to do stuff like this.(7 votes)
- Math is not my greatest subject at school could someone help me with math please.(5 votes)
- excuse my name but I need help on solving for the x-int(4 votes)
- What grade level is this for?(4 votes)
- Can you recommend a video that doesn’t talk about a number line but only how to solve the equation on a graph? Thanks.(3 votes)
- The are 48 learners in a classroom. Two bought a cake a cut into 13 pieces. Express the number of learners in ratio who did not get cake.(3 votes)
- this isn't in the video but how would you solve a problem where there is like kids and adults going to a play and the tickets are different costs and they have to get a certain amount of money??(3 votes)

## Video transcript

We're asked to represent the
inequality y is greater than 5 on a number line and on
the coordinate plane. Let's do the number
line first. Let me just draw out
a number line. That's my number line, all
the possible values of y. Let's make that 0 on
the number line. We could obviously go into
negative numbers, but we're going to be greater than
5, so I'll focus on the positive side. So let's say that's 1, 2, 3,
4, 5, and then 6, 7, so forth and so on. This number line represents y,
and y is going to be greater than 5, not greater
than or equal to. So we're not going to be
including 5 in the numbers that can be y. So we're not going to include
5, so we're going to do an open circle around 5, and all
of the other values greater than 5 will be included. So if there was a greater than
or equal to sign, we would have filled it in, but since
it's just greater than, we're not including the 5. So we've represented it
on the number line. Let's do the same thing on
the coordinate plane. Let me draw a coordinate
plane here. I'm just using the standard
convention. That is my y-axis right there. And then the horizontal axis,
I'll just assume is my x-axis. Let me draw some y values,
positive y values. 1, 2, 3, 4, 5. That is 5 right there, and you
go 6, 7, you can just keep going into larger and
larger numbers. And we want y to be greater than
5, so it's not going to be greater than or equal to. So we're not going
to include 5. So at 5, at y is equal to 5,
we will draw a dotted line. That shows that we're not
including y is equal to 5, but we want include all of the other
values greater than 5. So that we will shade in. So here we have shaded in all of
the values greater than 5. If it was greater than or equal
to 5, we would have drawn a bold line over here. So no matter what x is, no
matter what x we pick, y is going to be greater than 5.