How are the graphs of the functions y=x+7 and y=x-5 related?

They are both straight lines and parallel to each other. Their slopes are the same.

y = mx + b is one general form of the equation of a straight line,.

if we compare this to y = x + 7 and y = x - 5 we see that they both have the same slope of 1.

y = x + 7 will have a y intercept of (0,7) and y = x - 5 has y intercept of (0,-5)

They have the same slope, but different y-intercepts, making them parallel.