If you replace the x and y in the equation with points x and y of point (35, 30) and change the 10 to b you can solve for b which is the what changes from the original equation to this one.
30 = 5/7(35) + b
30 = 25 + b
5 = b
Since the equations are parallel they have the same slope.
This is the equation for a parallel line that passes through point (35, 30):
