The Most Useful Equation in Physics (Apparently) and Mathematics

Today I had my first 5th year Physics class and let me tell you, it was extremely interesting and stimulating. Now that on reflection though however, science isn’t for everyone. Anyways, I was taught as to why a certain equation is written that way and since today is pretty slow in science and technology, I’m going to teach you too!


The afromentioned equation is called the equation of a line and it is represented by y = mx + c.


Does everyone know what a graph is? If you do great. If you don’t look one up for reference. There are two axis on every single graph that are called the x-axis and the y-axis. (They can be called something else depending on what you’re doing) The equation of a line is an example of a linear equation, an equation that gives a straight line when plotted on a graph. Imagine that there are no numbers in y = mx + c. When this equation is plotted on the graph it intercepts 0 on both axis’s…axi…whatever the plural is. If you find a number on the x line to represent x and see what the y representation is, it always come out as the same number. This can be shortened down by saying that y = x.


That’s all fine and dandy till we remember that we are missing the m and + c. Take the equation y = x again. Now what if you say y = x + 1? What would happen to graph? Look at a graph or draw one to see. Done? You sure? Awesome. The line intercepts 1 on the y-axis and continues to be a straight. Linear equations are always straight lined graphs. If you try to see what x is now, when you get to y you will find it is no longer the same. It will always be one higher. Why? It intercepted 1 on the y-axis. It is exactly the same if the number was 10, 232, 100000, or even 10^9/4*3.14 . Wherever the number intercepts, it will always be that number higher than x. This number is represented by c. We have y = x + c .


The next piece of the puzzle is the letter m. This is the slope of the line which refers to the steepness of the line. It is commonly calculated by using rise/run.

Where rise being how far up you’re going. (y-axis)

Where run being how far along. (x-axis)

This is the simplist way, I find, to obtain the slope of a line. Another way of, using the graph in our heads, is by imagining at any point along the line, we draw a line down and connect it back to the line making a triangle. You count how many blocks you’ve come down and how many across to get the slope of the line. For example is you come down 3 blocks and go across 3, your slope is 3/3 which is 1. If you come down 4 and across 2, your slope is 4/2, which is 2.


And so we have it, the equation of a line : y = mx + c.


-Edward O’Neill


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