I stumbled across this page at Khan Academy:
The first equation shown to me was -2x=-12 (or something very similar). (The equation shown first seems to be random.)
At first, being in a stupor after final exams this week, I thought I should get the equation into y=mx+b form so maybe it should be y = 2x – 12. But the graph on the page doesn’t go to -12 so I quickly realized my error. Of course, if you solve for x, it is x = 6 which is a vertical line.
On the page, there is a video under the title “Stuck? Watch a video.” I started it and the first sentence was “…any linear equation can be written in the form y is equal to mx plus b”. Hmmm. No where in the video did it mention vertical lines.
So, if some student happened to get -2x=-12 and got stuck, and then watched the video hoping to find out how to graph it, they would have spent 11 minutes without their question being answered. I just found another Khan video about graphing lines…9 more minutes and no mention of vertical lines. I’ve watched (ok…fast forwarded through) a few videos at Khan and I still can’t find one that talks about vertical lines. I’m sure one must be there somewhere.
Here are the hints you can get about the -2x=-12 line:
- Notice that there is no y in this equation. Try solving for x and see what happens.
- Divide both sides by −2:
- This equation represents a line where all of the points have x=6.
- Let’s pick some points where x=6. (6,−5), (6,3) and (6,5) are all good choices.
- We can see that these points line up to form a vertical line that crosses the x-axis at (6,0).
I can hear students now: Why is there no Y? What is the slope? I have questions!
Also, for some reason, none of the equations are in the form y=mx+b…they add the additional burden of solving for y before I can begin the task of graphing them. I was able to do them in my head, but now some students will have to break out a pencil and paper (or click on the hints) to get it in the correct form. This is supposed to be practice of graphing the equations, but it actually includes extra algebra which is just tedious and not directly necessary to the task at hand. If I was a teenage algebra student, I would probably be bored and aggravated.
So, while this section would be good for practice or assessment in some areas, it may not be the best for initial instruction.
It is little frustrations like this that can annoy students (and teachers) and shows just how difficult good teaching can be…especially trying to teach using video.