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# Perpendicular lines from equation

## Video transcript

we are asked which of these lines are perpendicular and has to be perpendicular to one of the other lines you can't be just perpendicular by yourself and perpendicular lines just so you have a visualization for what perpendicular lines look like two lines are perpendicular if they intersect at right angles so if this is one line right there a perpendicular line will look like this a perpendicular line will intersect it but it won't just be any intersection it will intersect at right angles it will intersect at right angles so these two lines are perpendicular now if two lines are perpendicular if the slope of this orange line is M so let's say it's equation is y is equal to M X plus let's say it's b1 so it's some y-intercept then the equation of this yellow line its slope is going to be the negative inverse of this guy this guy right here is going to be Y is equal to negative 1 over M X plus some other y-intercept or another way to think about it is if two lines are perpendicular the product of their slopes is going to be negative one and so you could write that there M times negative 1 over m negative 1 over m that's going to be these two guys are going to cancel out that's going to be equal to negative 1 so let's figure out the slopes of each of these lines and figure out if any of them are the negative inverse of any of the other ones so line a the slope is pretty easy to figure out it's already in slope-intercept form its slope is 3 so line a has a slope of 3 line B it's in standard form not too hard to put it in slope intercept form so let's try to do it so let's do line B over here line B we have X plus 3y is equal to negative 21 let's subtract X from both sides so that it ends up on the right-hand side so this we end up with 3y is equal to negative x minus 21 and now let's divide both sides of this equation by 3 by 3 and we get y is equal to negative one-third X minus seven so this characters slope is negative 1/3 so here M is equal to negative 1/3 so we already see they are the negative inverse of each other you take the inverse of three it's 1/3 and then it's the negative of that or you take the inverse of negative 1/3 it's negative three and then this is the negative of that so these two lines are definitely those two lines are definitely perpendicular perpendicular let's see this third line over here so line see line C is 3 X plus y is equal to 10 if we subtract 3x from both sides we get Y is equal to negative 3x plus 10 so our slope in this case is negative 3 so our slope here is equal to negative 3 now this guy is the negative of that guy this guy's slope is a negative that but not the negative inverse so it's not perpendicular and this guy is the inverse of that guy but not the negative inverse so this guy is not perpendicular to either of the other two but line a and line B are perpendicular to each other