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We're asked what is the equation of line B?

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And they tell us that line A has an equation y is equal to

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2x plus 11.

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And they say that the line B contains the

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point 6, negative 7.

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And they tell us lines A and B are perpendicular, so that

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means that slope of B must be negative

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inverse of slope of A.

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So what we'll do is figure out the slope of A, then take the

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negative inverse of it.

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Then we'll know the slope of B, then we can use this point

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right here to fill in the gaps and figure out B's

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y-intercept.

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So what's the slope of A?

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This is already in slope-intercept form.

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The slope of A is right there, it's the 2, mx plus b.

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So the slope here is equal to 2.

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So the slope of A is 2.

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What is the slope of B?

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So what is B's slope going to have to be?

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Well, it's perpendicular to A, so it's going to be the

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negative inverse of this.

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The inverse of two is 1/2.

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The negative inverse of that is negative 1/2.

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So B's slope is negative 1/2.

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So we know that B's equation has to be y is equal to its

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slope, m times x plus some y-intercept.

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We still don't know what the y-intercept of B is, but we

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can use this information to figure it out.

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We know that y is equal to negative 7 when

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x is equal to 6.

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Negative 1/2 times 6 plus b, right?

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I just know that this is on the point, so this point must

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satisfy the equation of line B.

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So let's work out what b must be-- or what b, the

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y-intercept, this is a lowercase b, not the line B.

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So we have negative 7 is equal to-- what's negative

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1/2 half times 6?

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That's not a b there, that's a 6.

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What's negative 1/2 times 6?

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It's negative 3, is equal to negative 3 plus our

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y-intercept.

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Let's add 3 to both sides of this equation, so if we add 3

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to both sides-- I just want to get rid of this 3 right here--

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what do we get?

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The left-hand side, negative 7 plus 3 is negative 4, and

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that's going to be equal to-- these guys cancel out-- that's

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equal to b, our y-intercept.

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So this right here is a negative 4.

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So the equation of line B is why is equal to-- its slope is

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a negative inverse of this character-- so negative 1/2,

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negative 1/2 x.

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And its y-intercept we just figured out is negative 4.

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And we are done.

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