Learn what slope is

Hey class, my name is Professor Michael Donaher. Today you are going to learn about slope: why it is important, what it is, and how to find it and use it in math.

Slope matters because it tells us (in a mathematical sense) how much y increases over x. In real life, slope can tell you a rate of growth, how steep a mountain is, or any any situation where a rate of growth (or decline) is needed. So if you want to know how much money you can make for each unit of lemonade you sell at your lemonade stand, or if a mountain is too steep to climb, learn slope.

Slope = rise/run. One can find the rise by counting how many y values the graph goes up or down from one point to the next. The run can be found by counting how many x values to the left or the right the next point is. In real life scenarios, it may be better to think of it as change in output / change in input.  Here is an image to help you visualize it.


Slope will be an important concept to learn as you advance to more complicated math classes. One can use slope to graph a linear function, find rates of change, and solve for other points on the graph.

Just to make sure you understand, lets use an example. Suppose you have the following table.

These values can represent almost anything. But lets do some calculating. The original x value is 3. The second x value is 4. The difference here is one. This is the run because as I previously mentioned, the x values are inputs. As 3 moves to 4, 7 moves to 10. This is a difference of 3, therefore rise over run is 3/1, or just 3. This means the slope is 3.

Now, you can master calculating slopes. It may not seem how important this lesson is as for how it will impact your future careers. I understand that, and for many of you, you will not be finding slope during your jobs as adults. However, quantitative thinking like this is valuable to all types of problem solving and a variety of disciplines. Knowing what slope is will serve you in several social sciences that rely heavily on data analysis.

Our next lesson will be about slope-intercept form, so you can get a jump start on that by watching this Youtube video, where a funny many with a southern accent teaches the basics.

https://www.youtube.com/watch?v=u3spOO-m_Gg