once the bell rings just give me a second i'm not going to take too much longer i'll go through this as quickly as possible but ladies and gentlemen you have to understand something what we're doing right now is we're writing new equations of lines new equations of lines come in the form in slope-intercept form of y equals mx plus b all right where m is your slope and b is your y-intercept now the problem asks us to find a perpendicular line the thing we know about perpendicular lines are they have opposite reciprocal slopes so if i want to find the perpendicular line for here for this equation well this equation i know my slope is negative 2 right so what is the reciprocal of negative 2 well it's going to be 1 over negative 2. however perpendicular lines are opposite reciprocal meaning if one slope's negative the perpendicular slope is going to be positive so therefore the new slope of my line the new slope of my line is going to be y equals one half x plus b i did put a number in for b because i don't know what the new y intercept is all right i don't know if my y-intercept is 4 or not it could be it could not but don't put 4 just because you know that's the y-intercept of your original equation you would have to find what our new y-intercept is so now that we know now that we know what our our new slope is i can plug in a point into my x and y and solve for my b so remember each coordinate point has an x and a y coordinate so you plug in negative 3 in for x and negative 2 in for y therefore i get negative 2 equals a negative three halves plus b you guys okay okay so now i'll add three halves okay add three apps on both sides that's right um okay last thing guys to quickly go ahead and without showing you how to do fractions we know that this three halves is the same thing as 1.5 right so negative 2 plus 1.5 is going to be a negative one-half so negative one-half equals b therefore now i know what b is my negative one-half so my equation is y equals one-half x minus one-half