Hello, we're going to look at point slope form of a line. This form of a line is incredibly useful if we know a given point on the line and the slope. So M is the slope and X1 Y 1 is a known point. X1Y1 is any known point on the line. We're also going to look at parallel lines and perpendicular lines. Parallel lines are two lines that have the same slope, so lines that have the same slope. Perpendicular lines are going to be lines that have negative reciprocal slopes. Sometimes the symbol for perpendicular looks like an upside down capital T, but perpendicular lines have negative reciprocals as their slopes. What that really means is that the two can multiply together to give us one -1. So the two numbers, IE 3/4, it's perpendicular slope would be -4 thirds so that when the 2 multiplied together we would get -1. Also, horizontal and vertical lines are perpendicular. We're going to look at a couple examples, and the example we're going to do first of all is just going to be giving an equation in point slope form and identifying what the slope is and what the point is. This is in point slope form. So our slope is 6 and our known point is going to be 8 negative 5. Sometimes I suggest to people who struggle with this think about what makes this inside parenthesis go to zero that occurs when X equal 8. And also think about what makes this y + 5 go to 0 and that would be when Y equal -5 from point slope form. We could actually put this into standard form. Standard form would say we need to have the X's and Y's on the same side together and X needs to be positive. So in this case I'm going to move the Y to the other side and I need to have all the numbers without a variable on one side. So standard form in this case would be 53 equal six X -, y. We can also put this in slope intercept form. Slope intercept form says solve for Y. So we get Y equal six X -, 53. We're also wanting to look at if we're given a point and given a slope such as three -4 and a slope of 4 sevenths, can we put it into point slope form? This is one of the reasons point slope form is so powerful is we can use any point. We no longer have to have AY intercept. So y - -4 equal 4 sevenths times the quantity X -, 3 that's taken a point we know and a slope we know, and putting it into point slope. Well, what if instead we were given two points? If we have two points, we're going to start by finding the slope, and the slope is just the difference of the YS divided by the difference of the X's. Remember, up and down has to come from the same point. So if we're looking at this, we're going to get 3 / -3 or a slope of -1. So now I could put y - -4 equal negative One X - -2 or this is really important, I could use the other point y - -7 equal -1 * X -, 1. You might think that those don't look at all the same, but if we put them in point slope form, no. If we put them in slope intercept form, that's a positive two times a -1. We'd get Y equaling -1 X -6 for this one, and we would get Y equal negative X -, 6 for this one. The same exact equation using either of the two points because the two points are both on the line. The last thing we should talk about is what if we know the two points on a line, but we want it parallel to another point? So say we have a .35. If we know the slope going through these two points is -1. If we want it parallel, we're going to use the same slope that we just found and use point slope form y -, 5 equal -1 X -3. What if we wanted it perpendicular? Doing the exact same concept, but now we're going to look at perpendicular slope. How did we find the perpendicular slope? We took the negative reciprocal. Well, what's the negative of 1 / -1? That's just +1. So in point slope form y -, 5 equal +1 X -3. Thank you and have a great day.