I’m interested for personal reasons on how these mathematical operations work. I know they’re quite simple, but I never quite understood them, so it’s something that got stuck with me. Any explanations are welcome!
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Get a piece of graph paper. Now draw a small line segment on it, maybe an inch long or so. A little to the left of the line draw a vertical line that starts below your line segment and finishes above it. Now at the bottom of that vertical line draw a horizontal line to the right that finishes past your line segment. You should have something that vaguely looks like the (horrible) diagram below.
Y
l
l /
l
———- X
We can label these things now. The horizontal line we will call the x-axis. The vertical line we will call the y-axis. The point at the bottom where the two lines meet we will call the origin.
Starting at the origin, move to the right on the x-axis until you are below the bottom of the line segment you drew. Now move up from that point until you reach your line segment. The point where you end up can be defined by (X,Y) where X is the number of spaces you moved to the right, and Y is the number of spaces you moved up. You can define any point on your line with two numbers X and Y in the format (X,Y).
Now because of algebra we can use the x and y values in a formula, y=mx+b, that defines your line. The formula is called a linear equation. X and Y are points on the line, m is the slope of your line, and b is where the line crosses the y axis, or the y-intercept. The slope is just how much over and up you need to move to get to the next point on your line. Now we can use that formula to do math things.
edit: Let me work on formatting this.
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