A few days ago this week, I was tutoring a student in a public library, and a few minutes into the lesson, an older gentleman happened to seat himself next to us. I didn't give him much notice and was focused on my student who was trying to find the slope of a line. The slope was obviously zero, but my student was painstakingly finding the 'run' of the slope. I was a little impatient and said something mathematically inaccurate. "The denominator doesn't matter. Look, the numerator's zero, which means the slope is zero." Of course, my student quickly nodded and agreed with whatever I said. My focus was zoomed in on showing him how to find the slope of a line perpendicular to the first line when the man sitting next to us tapped me on the shoulder and said, "The denominator doesn't matter assuming..." "...It is a non-zero real number," we said in chorus. I sheepishly thanked him and redirected my reddened face at my student. I was so embarrassed because... read more