Equations of Perpendicular Lines

Why might we want to consider the relationship between the coefficients of x and y?

There are many solutions but not infinite

1 x + 2 y = 4
-6 x + 3 y = 5

2 x + 3 y = 9
-6 x + 4 y = 8

Any solution where the x and y coefficients swap and one is negative. Students will need to use multiples to avoid repeating values. The constant term can take any remaining value.