Question

write the equation of a line that is parallel to the line y=x-6    How do you do this without a point?

Answer 1

The question asks for “a line” not “the line” so you provide an example. All parallel lines have the same slope, so the slope here is 1. The simplest equation is y=x, but y=x+a where a is a number, is the general equation for all parallel lines with slope=1.