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Hello and welcome.
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We are looking at chapter 8, section 1.
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This is problem 5.
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So we're asked to describe and sketch the surface in 3d representing this equation here, x plus y equals 2.
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So i think the best way to graph this is to start in two dimensions.
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So if we graph x plus y equals 2, we can get the intercepts.
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So here's two.
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Both intercepts are positive 2.
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And we connect the dots there.
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And so it looks like this.
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So notice this is my x -axis and this is my y -axis.
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This is r -squared, two dimensions.
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Now, if we take that idea and just extend it into three dimensions, graphing this actually isn't too bad.
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So first things first, this is going to be our x -axis, and this is going to be our y -axis.
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This will be our z -axis.
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So notice the x -and -y -axis are still there.
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So what i want to do is i want to start by just copying this onto my graph here.
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So i'll try to put one, two, two.
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So i'm just plotting those two points on positive two and positive two on the x and positive two on the y.
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I'll connect my dots here.
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And so the next step is how we make this into three -dimensional.
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Because this actually isn't done yet...