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A line has a slop of negatave 3/4ths, and goes through the point (0,8).

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What is the equation of this line in slope-intercept form?

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So any line can be represented in slope-intercept form as y=mx+b.

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Where this 'm' right over here, that is the slope of the line, and this

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'b' over here, this is the y-intercept of the line.

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Let me draw a quick line here just so that we can visualize that a little bit.

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So that is my y-axis, and then that is my x-axis.

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And let me draw a line, and since our line here has a negative slope,

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I'll draw a downwards sloping line.

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So let's say our line looks something like that.

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So, hopefully we're a little familiar with the slope already,

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the slope essentially tells us, look start at some point on the line,

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and go to some other point on the line,

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measure how much you have to move in the x-direction, that is your run,

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and measure how much you have to move in the y-direction, that is your rise,

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and our slope is equal to rise over run. And you go see over here, it will be

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downward sloping, because if you move in the positive x-direction,

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we have to go down. If our run is positive, our rise here is negative.

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So this will be a negative over positive, and will get a negative number

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Which makes sense, because we're downward sloping.

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The more we go down in this situation, for every step we move to the right,

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the more downward sloping we'll be; the more negative of a slope we'll have.

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so that's slope. That's slope right over here.

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The y-intercept just tells us where we intercept the y-axis.

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So the y-intercept, this point right over here, this is where the line intersects

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with the y-axis. This will be the point (0,b).

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And this actually just falls straight out of this equation.

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Let's evaluate this when x=0.

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y=m*0+b, well anything times zero is zero, so y=0+b or y=b, when x=0, so this is

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the point (0,b)

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Now, they tell us what the slope of this line is.

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They tell us a line has a slope of -3/4 so we know that our slope is -3/4

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And they tell us that the line goes through the point (0,8)

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They tell us we go through the, let me just do this in a new color

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I've already used orange, let's use this green color.

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They tell us that we go through the point (0,8) notice x is 0, so we're on the y-axis

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when x is zero, we're on the y-axis, so this is our y-interecept

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so b, we could say, we could do a couple of-- our y-intercept is the point (0,8),

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or we could say b, remember, it's also (0,b) we could say b=8

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So we know m=-3/4, and b is equal to 8, so we can write the equation of this line.

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in slope-intercept form.

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It's y=-3/4 times x, plus b, plus 8. And we are done, we are done.