The best way to describe lines y = x+3 and - x+y=7

Parallel lines

Step-by-step explanation:

The equation of a line in slope - intercept form is

y = mx + c (m is the slope and c the y - intercept)

y = x + 3 ← is in slope - intercept form

with slope m = 1

- x + y = 7 (add x to both sides)

y = x + 7 ← in slope - intercept form

with slope m = 1

Parallel lines have equal slopes, thus the lines are parallel