I remember being slightly giddy the first time I was told that the equation of the line with x-intercept a and y-intercept b is $\frac xa + \frac yb = 1.$ I love this equation and the generalizations it implies. My guess is that less than one percent of the algebra students in a school would be impressed with this equation. So, occassionally, I teach to the one percent. Not really for them, but because I get a kick when that one student gets that look on his/her face.

I remember being slightly giddy the first time I was told that the equation of the line with x-intercept a and y-intercept b is $\frac xa + \frac yb = 1.$ I love this equation and the generalizations it implies. My guess is that less than one percent of the algebra students in a school would be impressed with this equation. So, occassionally, I teach to the one percent. Not really for them, but because I get a kick when that one student gets that look on his/her face.

I got to thinking about this. If you can find two "nice" points $(x_1, y_1)$ and $(x_2, y_2)$, then the equation of the line passing through those two points is $$\frac{x-x_1}{x_2-x_1} + \frac{y-y_2}{y_1-y_2} = 1$$