Blog Post 4-Adrian Simion

Adrian Simion

Blog Post #4- Learning about Slope and How to correctly find it!

       Good afternoon my fellow students! How is everyone doing today? I am Professor Simion, but you can all call me Adrian instead because it makes me feel young. Today's class lecture will consist of learning about what slope is, and how to find slope by reading any linear graph given to you. You will essentially learn the necessary skills to finding the slope of a function. I know this may sound very complicated and difficult to do, but I will give you students simple step by step instructions on how to do so and before you know it you'll be finding slopes all on your own with complete ease.           So the first question you all may ask is What is slope? Well very good question indeed class. You see students the definition of Slope: is a number that measures its steepness, usually denoted by the letter m. It is the change in y for a unit change in x along the linear line. 

       

      Now you see students that there are also four types of slope that you will most likely encounter when reading a linear graph. There are Horizontal slopes, Vertical slopes, Positive and Negative slopes. A positive slope (Uphill) is a linear line that runs upwards on the graph and has a positive m. A negative slope (Downhill) is exactly the opposite of a positive slope and has a -m, or a negative linear line that runs downward on the graph. Horizontal slope is a linear line that runs straight across on the graph and has no height to it whatsoever so Slope=0. Lastly a Verticle graph is a linear line that run straight up and down only.

     Look at the equation Y=mx+b, where m represents the slope of the plotted line. M also represents by how much the line will rise/fall and by how much the line will run on the graph. While b represents the point on which the linear graph will cross the Y-axis. Now to find the equation of a slope you can use one of two methods. 

        The first method is to use simple counting techniques. For more simple lines you can pick a place on the graph and either go up or down to find the height and then straight across the graph to another point to locate the width. Use the rise over run method to set it in slope form.  For example: simple counting such as below can help you find the slope. Going up two places gives you the rise=two, then run across the line to a new point on the graph will give you the width which is three. You now simply place place rise over run and now you have figured out the slope of the graph. The answer would be slope= 2/3. Did you all see how I got that? Please feel free to ask questions if you did not!

         The second method of finding slope is by following an equation. The equation          M=(y2-y1)/(x2-x1) is a method of finding slope by locating any two different point on the linear graph. Now you use the x and y of those two point and you plug them into the equation. You must start with finding the Y axis first before moving on to find the X axis. Note which ever side you choose first, you must follow the same routine and choose the same point you started with. So if you start with 3-1 for example you must then start from the same place and use 0-4 instead of 4-0. You must go the same direction to do the equation correctly. If not you will not get the actual slope of the graph. Use the picture below for further explanation. After finding both the Y point and X point from the equation you simply just put Y/X to find slope or rise over run. As you can see below how its done, -2/4 is the answer and also observe that the linear graph is pointing down and making it a negative graph as explained above. This would then make you Y negative resulting in a -2 for the top part of your slope equation. So what does your findings mean when graphing? It means that you move down 2 and then over 4 and continue this cycle to create dots on the graph. Now take a ruler and by connecting the linesman a linear line with your new found slope. You now know how to both find slope and also how to graph slope as well.

         So now students you have learned what slow is, the types of slope that exist, how to graph slopes, and lastly how to find slope two different ways. If you have any further questions feel free to email me or come to my office hours. Thats all for today class! You are all dismissed, and see you all next class.