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We're asked to represent the inequality y is greater than 5

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on a number line and on the coordinate plane.

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Let's do the number line first.

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Let me just draw out a number line.

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That's my number line, all the possible values of y.

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Let's make that 0 on the number line.

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We could obviously go into negative numbers, but we're

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going to be greater than 5, so I'll focus on

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the positive side.

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So let's say that's 1, 2, 3, 4, 5, and then 6, 7, so

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forth and so on.

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This number line represents y, and y is going to be greater

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than 5, not greater than or equal to.

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So we're not going to be including 5 in the numbers

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that can be y.

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So we're not going to include 5, so we're going to do an

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open circle around 5, and all of the other values greater

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than 5 will be included.

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So if there was a greater than or equal to sign, we would

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have filled it in, but since it's just greater than, we're

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not including the 5.

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So we've represented it on the number line.

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Let's do the same thing on the coordinate plane.

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Let me draw a coordinate plane here.

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I'm just using the standard convention.

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That is my y-axis right there.

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And then the horizontal axis, I'll just assume is my x-axis.

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Let me draw some y values, positive y values.

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1, 2, 3, 4, 5.

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That is 5 right there, and you go 6, 7, you can just keep

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going into larger and larger numbers.

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And we want y to be greater than 5, so it's not going to

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be greater than or equal to.

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So we're not going to include 5.

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So at 5, at y is equal to 5, we will draw a dotted line.

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That shows that we're not including y is equal to 5, but

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we want include all of the other values greater than 5.

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So that we will shade in.

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So here we have shaded in all of the values greater than 5.

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If it was greater than or equal to 5, we would have

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drawn a bold line over here.

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So no matter what x is, no matter what x we pick, y is

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going to be greater than 5.

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