Solving and graphing linear inequalities
About this video
Sal represents the inequality y > 5 in two ways. On a number line he draws an open circle at 5 and includes everything to the right. On the coordinate plane he draws a dotted horizontal line at y = 5 and shades everything above it, since y is greater than 5 whatever x is.
You'll be able to
- graph a strict inequality like y > 5 on a number line using an open circle.
- graph y > 5 on the coordinate plane with a dotted line and shading.
- explain when to use open versus closed circles and dotted versus solid lines.
Key words
- inequality
- A statement that one quantity is greater or less than another, like y > 5.
- open circle
- A hollow circle on a number line showing that number is not included.
- dotted line
- A dashed boundary line on a graph showing points on the line are not included.
- coordinate plane
- A grid with an x-axis and a y-axis for plotting points (x, y).
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.
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