How to Put Perpendicular Lines Into Standard Form

Hi, I'm Rachel, and today we're going to be going over how to put perpendicular lines into standard form. So, again, perpendicular lines are lines that make a right angle, 90 degrees. And, the slope is always the negative reciprocal of the other line. So, for example, if you have the line Y equals five X plus three, the negative reciprocal of five is negative one fifth. So, the slope of the perpendicular line will be Y equals negative one fifth X and then the Y intercept can be anything, so we'll say plus 10. Now, to get these lines into standard form from slope intercept form, which is what they're in now, we want to put it into the form Ax plus By equals C. That's what we call standard form. So, let's start with this one, the first line. We are going to move it over, the X, right, so we get on this side. So, we have, we subtract five X, we have negative five X plus Y equals three, and that is standard form for this line. And for this line, we'll add one-fifth X to both sides, so we get one-fifth X plus Y equals 10. And, to make it look a little nicer in standard form, we generally wanna get rid of the fractions, so we'll multiply it, both sides of the equation by five, and we'll end up with X plus five Y equals 50. And, here are the two standard forms of the perpendicular lines. I'm Rachel, and thanks for learning with me today.