Question 30951
Hey Cody.  Your teacher is indeed correct

the original equation {{{y=(4/5)*x+9}}}

you had the right idea when you got to

{{{(-4/5)x+y=9}}} multiply through by 5
{{{-4x+5y=45}}}  multiply through by -1, this switches the signs of all the terms to give you
{{{4x-5y=-45}}} 
You algebra is correct but you forgot to multiply the 45 by the negative 1