Question

Y - 4 = - (1)/(4) (x-0)

I came up with: -4y + 16 = X
I continued to Standard form (Ax+Bx=C); X-4y=16

book has: 4y-16 = -X
X + 4y = 16

Answer 1

Your first solution (\(-4y + 16 = X\)) is the same as theirs, they just chose to leave the negative sign on the X.

Your second solution has a slight sign error -- you move the 16 over to the right and then the X to the left (here it is done with both their form of the equation and yours):

\[\begin{align} 4y - 16 &= -x & -4y + 16 &= x \\4y + x &= 16 & -4y - x &= -16 \\x + 4y &= 16 & 4y + x &= 16 \end{align}\]