 This video will talk about parallel and perpendicular slopes. Parallel lines, if you look at two parallel lines, remember slope is the rate, and these two lines are going at the same rate, so they have the same slope. If I draw a perpendicular line in here to these two lines, remember perpendicular lines have a right angle. Well this one has a, the blue one has a positive slope, and this green one is going down, so it has a negative slope. So I know that they are going to be opposites of each other, and if I were to actually give you those slopes, you'd find out that they are opposite reciprocals. So for instance, I could say that maybe this slope right here is going to be maybe positive two, then if that were true, then this slope over here would be a negative reciprocal of two, which is one-half. And it asks us, how do we know that all horizontal lines are parallel? Well, a horizontal line is straight across, and another one is going to be just like it, also straight across, and if they are both doing the same thing, their rates are both zero in this case, so we know that they are parallel lines. So line one contains zero, zero, and negative two, four. And line two contains one, negative five, and negative one, negative one, and we want to know if they are parallel, perpendicular, or neither. Well we need to know their slopes. So let's find the slope of line one. So line one slope is going to be y minus y, four minus zero, over x minus x, and negative two minus zero. So that's four over negative two, or it's just negative two. And if I do the other one, l two slope is going to be negative one minus a negative five, which is really plus five. And the x's would be negative one minus one. So negative one plus five is going to be four, and negative one minus one is going to be negative two, which reduces to negative two. So we know these are parallel because their slopes are exactly the same. This example says slope of line A is three-fourths, and the slope of line B is four-thirds. And are these two parallel, perpendicular, or neither? So they're reciprocals of each other, but they're not negative reciprocals of each other. So these two are neither. So now we have some equations of lines, and we want to know if they're parallel, perpendicular, or neither. So if I look at this one, it's y equals slope times x plus b, so I know that the slope here is negative six, and the slope here is negative six, so they're the same slope. So we know that they are parallel. Now this case I'm going to have to solve for y. So I'm going to subtract the x from both sides, and that'll give me three y equal to negative six minus x. And if I divide everything by three, then that tells me that y is equal to negative six divided by three is negative two, and negative x divided by three is negative one-third x. So this slope here is negative one-third, and the slope in this equation is a positive three, and they are reciprocals of each other, and they're also opposites of each other, one's positive, one's negative, so these are perpendicular. Y equal three is a horizontal line, so its slope is going to be zero. And then this is y equal three x, so its slope is equal to three. They're not the same slope, so they are neither.