You need to know that when 2 lines are parallel, they have the same slope.
Make sure your equation y = 3x - 8 is in slope intercept form (y = mx + b), which it already is.
m = slope, b = y-intercept, (x,y) = point that the line passes through
My slope for this line is 3 (number in front of the x variable), so my new equation has to have a slope of 3 as well.
Write down new equation w/ new slope y = 3x + b and plug (1,8) into (x,y). That'll give me:
8 = 3(1) + b, which simplifies to 8 = 3 + b, so b = 5. My new y-intercept is 5. Put everything together and you'll get.
y = 3x + 5
Hope this helps.