For those who’d like a very fundamental and rudimentary explanation for slope and how to understand it as a function of two given variables, (and naturally, a correlation between that and real life), imagine the following:

Start walking for a good minute. Pick up the pace for another minute. Stop for a minute. Walk backwards for a couple more minutes. Then, walk forward for a few more.

In this scenario, as time (your x) increases, the line drawn will have different pieces varying on your movement or distance traveled (your y):

- it’s “going up” (in a positive direction, sometimes at a larger angle depending on how quickly you walked)
- it’s “going down” (in a negative direction, again depending on whether you paced or moonwalked)
- it flattens out (a representation of not moving whatsoever)

Even with that last one, your x variable time doesn’t actually stop, so your line doesn’t just cut abruptly away. The pencil keeps moving.

In the fourth case, and this is probably the best way one can explain in real terms the difference between no slope and undefined slope, the line just drops straight down or straight up. In other words, you moved to a certain distance … without respect to time. It’s as if you teleported in less than an instant.

And for now, that’s impossible.

In this life, we make many choices. Sometimes, our lives take divergent courses and other times they escalate to levels unforeseen. However or wherever we move, or even when we don’t, time will move on without us.

Maybe we should invest in making our slope positive. Continuously.

**Mr. V, watch the ripples change their size, but never leave the stream of warm impermanence …**

### About Jose Vilson

JosÃ© Luis Vilson is a math educator, blogger, speaker, and activist. For more of my writing, buy my book *This Is Not A Test: A New Narrative on Race, Class, and Education*, on sale now.

## Comments 5

Nice explanation on this! Sometimes, what we learned in the classroom applies not only in our test papers but also in our lives.

This resonated with me to the point where I quote you and send readers to your blog in my most recent blog post. I only hope my son (now 8) has a math teacher with such creativity when he is older. Great insight. I subscribed to your blog and look forward to reading more.

sorry, didn’t realize when i put my son’s age as eight it would show up as a smile.

Finally, this is the link to my novel.

Author

Thanks for reminding me. No more emoticons. Secondly, I’ll go read your blog and comment appropriately.