Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes so that 2 of the lines are parallel and the third line is a transversal that is as close to perpendicular to the parallel lines as possible.
Hint
What do we know about the slopes of parallel lines and transversals?
Answer
Since the slope of a perpendicular line should be the negative reciprocal of the other line, and since we can’t make it negative, then the slope that is closest to zero should be the closest to perpendicular. Accordingly, the best answer so far is 6x + 3y = 7, 4x + 2y = 8, x + 9y = 5
Source: Shelli Foust and Robert Kaplinsky
A slight modification using slope-intercept, standard and point-slope form of a line will make possible a perpendicular transversdal with digits 0 through 9. Extend or push DOK by wondering about maximizing or minimizing the distance between the parallel lines.
https://drive.google.com/file/d/1F-TzSHZG2qchQ1EZp5GuDk-8MofczjTW/view?usp=sharing
I think the above picture has a 1 where a box should be when I transferred from Desmos
Here is the open middle in desmos form.
https://teacher.desmos.com/activitybuilder/custom/638d4483b291ceac411c5ce3