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We are asked which of these lines are perpendicular.

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And it has to be perpendicular to one of the other lines, you

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can't be just perpendicular by yourself.

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And perpendicular line, just so you have a visualization

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for what for perpendicular lines look like, two lines are

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perpendicular if they intersect at right angles.

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So if this is one line right there, a perpendicular line

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will look like this.

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A perpendicular line will intersect it, but it won't

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just be any intersection, it will

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intersect at right angles.

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So these two lines are perpendicular.

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Now, if two lines are perpendicular, if the slope of

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this orange line is m-- so let's say its equation is y is

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equal to mx plus, let's say it's b 1, so it's some

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y-intercept-- then the equation of this yellow line,

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its slope is going to be the negative inverse of this guy.

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This guy right here is going to be y is equal to negative 1

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over mx plus some other y-intercept.

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Or another way to think about it is if two lines are

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perpendicular, the product of their slopes is going to be

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negative 1.

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And so you could write that there. m times negative 1 over

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m, that's going to be-- these two guys are going to cancel

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out-- that's going to be equal to negative 1.

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So let's figure out the slopes of each of these lines and

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figure out if any of them are the negative inverse of any of

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the other ones.

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So line A, the slope is pretty easy to figure out, it's

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already in slope-intercept form, its slope is 3.

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So line A has a slope of 3.

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Line B, it's in standard form, not too hard to put it in

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slope-intercept form, so let's try to do it.

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So let's do line B over here.

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Line B, we have x plus 3y is equal to negative 21.

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Let's subtract x from both sides so that it ends up on

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the right-hand side.

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So we end up with 3y is equal to negative x minus 21.

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And now let's divide both sides of this equation by 3

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and we get y is equal to negative 1/3 x minus 7.

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So this character's slope is negative 1/3.

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So here m is equal to negative 1/3.

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So we already see they are the negative

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inverse of each other.

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You take the inverse of 3, it's 1/3, and then it's the

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negative of that.

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Or you take the inverse of negative 1/3, it's negative 3,

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and then this is the negative of that.

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So these two lines are definitely perpendicular.

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Let's see the third line over here.

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So line C is 3x plus y is equal to 10.

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If we subtract 3x from both sides, we get y is equal to

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negative 3x plus 10.

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So our slope in this case is negative 3.

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Now this guy's the negative of that guy, this guy's slope is

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a negative, but not the negative inverse, so it's not

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perpendicular.

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And this guy is the inverse of that guy but not the negative

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inverse, so this guy is not perpendicular to either of the

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other two, but line A and line B are

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perpendicular to each other.

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