Hi welcome to MooMooMath. Today we are going to look at special slopes. I’m going to review the guidelines of slopes. This first example has a slope that is going up when you look from left to right so it is a positive slope and we always count our slope as rise over run. So in the first example we will rise positive 4 and run positive 3 so the slope is positive 4⁄3.Let’s look at the second example, if you move from left to right notice the line is going downward so it will have a negative slope. When we go to count it we will go down 2 and over 1, 2 so it will have a slope of negative 2 over 2 so it will have a slope of negative 1. Again the slope is negative and going down from left to right. Now let’s look at our two special cases. The first one does not go up or down but is horizontal. So any time you have a horizontal lie you have a slope of 0 why is that? You have a rise of 0 and a run of any value so our slope will just be 0. Let’s look at this last one. The equation for this line is y= positive 2. Whenever you have a horizontal line it is always y = the constant of where line crosses the y axis. In this case it crosses the y axis at 2. Now in the last case you have a vertical line. Now the vertical line does not have a slope, or sometimes they call it an undefined slope. Why is it undefined or no slope? We have a rise of any value but it has a run of 0 what do we know when we divide any value by 0? You can’t do that so that is why the value is undefined. So this crosses the X axis at two so the equation of the line is x equals two and no Y value. Let’s look at a summary of our slopes. So here is our Cartesian coordinate plane to find the slope from a to b we count our rise is 3 and our run is 4 so this line is ¾ our slope of our next line is down one over four so it is negative ¼. The slope of our special lines is: the vertical lines (C) are undefined slope or no slope and the slope of the horizontal line (d) is 0. The equation for line d is negative 2 y because that is where the line crosses the y axis a so it is y= negative 2 the vertical line (C) has an equation of x = negative 3 whenever you have a vertical line it is x equals and a horizontal line is y equals that constant. Hope this was helpful.