Learn about Slope of Parallel and Perpendicular Lines In this lesson let’s learn about slopes of parallel and perpendicular lines. We’ll do three problems and we need to determine whether the pairs of lines given to us are parallel perpendicular or neither. So we’ll do three. For one line is ab the other line is cd. So here’s what I’m going to do. First thing I’m going to find the slope of line ab, slope of line ab is y2–y1 over x2–x1 difference in y coordinates different in x coordinates. So ab so that’s here, right. So what’s the difference on the y coordinates between ab that’s 5-1, y2–y1. Similarly x2 is 1 and x1 is 2. What does this mean? So slope of ab equals 5-1 is 4, 1-2 is -1 which means it’s -4. So the slope of ab=-4 change the color let’s find the slope of cd which is again y2– y1 over x2– x1. So slope of cd equals y2–y1 that’s fine as this so -2-2 over 5-4. So -4/1 which is -4. Since slope of ab equals slope of cd both equals – 4 if slopes are equal the lines are parallel. So these two lines are indeed parallel so here the answer is these lines up parallel. Let’s try this second one here I’m going to do it a little faster we need FG and HJ so for FG the slope is y coordinate difference with 2–1 is 1, 2-1 is 1 which means the slope of FG=1. Slope of HJ is 2 -1 is 2-1=1 over 1-2 equals–1. So the slope here is -1. If the slope of HJ is -1 and the slope of FG = 1 right the key thing to remember if the slope of two lines when multiplied gives you -1 then the lines are perpendicular. If the slope of line 1 which is 1 times slope of line which is -1 if the multiplication of the two slopes equals -1, 1 times -1 is -1 then the lines are perpendicular so what have we learned these are perpendicular lines. The reason they’re perpendicular is because that slopes when multiplied give us negative one remember that. Let’s do the 3rd one, 3rd one says ab and cd this is ab, this is cd so what’s the slope of ab = 2-(-1) over 7-2 which is equal to 2 +1 is 3, 7-2 is 5. Slope of cd=-6 minus -3 over -3 minus 2 which is what -6+3 is -3 over -5 which is -3 over 5 that is +3 over 5 because these two get cancelled up. So since the slopes are equal right these two lines are parallel. Let’s double check our answer, -6 +3 is -3 and at the bottom I’ve got -3-2 is –5. -3, -5 gives you 3/5 same thing so the lines are indeed parallel. Key thing to remember, if we take any two points on a line or we take two lines and we take two points on the need of the lines and we compute their slope if the slopes are equal then they are parallel, if the slopes are not equal and multiplying them gives you negative one then the slopes or the lines are perpendicular.