How to write an equation of the line satisfying the given conditions?

Question

Through (3,7); parallel to 7x=8y+10

the equation of the line is?

Answer 1

The equation 7x = 8y + 10 is rewritten as y = (7/8)x - 5/4 so a parallel line has slope = 7/8

The new line equation is y-7 = (7/8)(x-3) = (7/8)x - (21/8) or y = (7/8)x -(21/8) + (56/8) = (7/8)x + 35/8

Check: y = (7/8)(3) + 35/8 = 21/8 + 35/8 = 56/8 = 7 OK!

So the new line equation is (7/8)x + 35/8