Chapter 5 - Thoughts About Slope

This was a short project, but an interesting one. I asked the students a few questions concerning slope, and they wrote explanations and comments.

Here is the assignment: "What is slope? When say that a line has a slope of 2:3, what does that mean? What is the slope of a vertical line? And what is the slope of a horizontal line? What is the difference between 1/0 and 0/1? Explain using examples from algebra and examples. Explain your answers, and draw diagrams of each."

Mark explained what slope is in the following paragraph, by relating it to stairs:

"The simplest way to define slope is 'steepness', so if you are walking up a set of stairs, we call the vertical part of each stair is the 'rise' and the horizontal part (where you put your foot) is the 'run'. Most sets of stairs have the same rise and run as other stairs, so people don't have trouble walking up and down. When you climb a ladder, the slope of the ladder is usually much steeper than stairs are, so we would say that it the ladder is at a steep slope. A standard stair has a 7 inch rise and a 10 inch tread, which means that each goes up 7 inches vertically, and the flat part where you put your feet is 10 inches."

In geometry, slope is just like steepness, so if a line is at a steep angle, the slope of the line might be the ratio 7:3 and if the line is at a less steep angle, the slope might be 2:3. If the line is horizontal, we say it has a slope of zero (also called 'no slope') and if it is at a 45 degree angle we should say it's slope is 1 to 1 (or just call it 1). If it is vertical, we might want to say that the slope is 1:0 but that is called 'undefined' because 1:0 means 1 divided by zero and you can't divide by zero.

He included some diagrams with his explanation: