Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the blanks to create two distinct perpendicular lines. Note that the coefficient for the second line’s y is negative.
__ x + __ y = __
__ x + -__ y = __
Hint
What do the equations of perpendicular lines have in common?
Answer
There are many answers but the coefficients of x and y for each line must produce a product of -1. For example, 2x + 3y = 5 and 6x + -4y = 7
Source: Bryan Anderson
If students know anything about equations of perpendicular lines then they must know about gradients or slopes of lines and also that the product of the slopes is -1. If they don’t then then are going to be using some other rule which doesn’t say anything else that is useful.
I don’t understand the first line of the answer.