Sorry about not posting a math tidbit yesterday. I came home and fell asleep. (I was up late two nights ago helping a student with a research paper, and it caught up with me last night. That’s a story for another post.)
Today’s tidbit, again, care of a number of my students who are studying hard for their finals, is about slope.
When I say “slope”, the first thing that should come to your mind immediately is “rise over run”. Somewhere along the way, some math teacher should have drilled this little phrase into your head.
If you can recite this when you are asked what slope is, then you’re a step ahead of the game, but do you actually understand what “rise over run” means? Some of you may say, “Sure. It’s y over x.”
All right, that now gives us two possible definitions for slope, but it still really doesn’t tell us much about why we know this.
Slope is really the change in the y-coordinate divided by the change in the x-coordinate, or (y2 – y1) over (x2 – x1).
This is also know as the slope formula. We can take any two points, label one of them Point 1 and the other Point 2, and plug them into the formula to find out what the slope for that line is. If you are just going to graph the slope, it is useful to leave your answer in the fraction so you can easily see how many spaces to move up and how many spaces to move to the right as you’re creating the points that make up the line. If you are putting it into an equation for a line, then go ahead and simplify it.
