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We're asked to graph the inequality y is less

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than 3x plus 5.

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So if you give us any x-- and let me label the axes here.

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So this is the x-axis.

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This is the y-axis.

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So this is saying you give me an x.

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So let's say we take x is equal to 1 right there.

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3 times 1 plus 5.

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So 3 times x plus 5.

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So 3 times 1 is 3 plus 5 is 8.

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So one, two, three, four, five, six, seven, eight.

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This is saying that y will be less than 8.

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y will be less than 3 times 1 plus 5.

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So the y-values that satisfy this constraint for that x are

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going to be all of these values down here.

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Let me do it in a lighter color.

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It'll be all of these values.

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For x is equal to 1, it'll be all the values down here, and

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it would not include y is equal to 8.

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Y has to be less than 8.

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Now, if we kept doing that, we would essentially just to

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graph the line of y is equal to 3x plus 5, but we wouldn't

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include it.

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We would just include everything below it, just like

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we did right here.

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So we know how to graph just y is equal to 3x plus 5.

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Let me write it over here.

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So if I were to write y is equal to 3x plus 5, we would

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say, OK, 3 is the slope.

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Slope is equal to 3, and then 5 is the y-intercept.

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Now, I could just graph the line, but because that won't

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be included in the y's that satisfy this constraint, I'm

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going to graph it as a dotted line.

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So we'll start with the y-intercept of 5.

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So one, two, three, four, five.

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That's the y-intercept.

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And the slope is 3.

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So if you go over to the 1, you go up 3.

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So let me do that in that darker purple color.

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So it'll look like this.

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It will look like that.

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That point would be on it.

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That point would be on it.

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If you go back, you're going to go down by 3.

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So that point will be on it, that point, and that point,

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and I'll just connect the dots with a dotted line.

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That dotted line is the graph of y is equal to 3x plus 5,

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but we're not going to include it.

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So that's why I made it a dotted line because we want

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all of the y's that are less than that.

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So for any x-- so you pick an x.

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Let's say x is equal to negative 1.

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If you evaluate 3x plus 5 for that x, you'd get here.

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But we only care about the y's that are

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strictly less than that.

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So you don't include the line.

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It's everything below it.

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So for any x you pick, it's going to be below that line.

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You take the x, go up to that line and everything below it.

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So for all of the x's, it's going to be this entire area.

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Let me draw it a little bit neater than that.

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It's going to be this entire area that's under the line.

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I'll do it in this orange.

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It's a little bit easier to see.

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So this entire area under the line is y is less than 3x.

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