If y = x - 6 were changed to y = x + 8, how would the graph of the new function compare with the first one?

The first one would have a y-intercept of (0,-6) and the second one would have a y-intercept of (0,8) and x (the slope) would still be the same.
y=x-6 would have points with (0,-6) (2,-4) (4,-2) (6,0)
y=x+8 would have points with (0,8) (-2,6) (-4,4) (-6,2)
In other words shifted up. Hope this helps!