Question 800584
In the form y=mx+c
m=slope and c=intercept (y @ x=0)

Original: 8x-6y=7 becomes {{{ y=(8/6)*x-7/6 }}}
At x=6 y=8-7/6=41/6
This is {{{ 41/6 + 1 = 47/6 }}} above (6,-1) 
Shift intercept down by this amount

New:
slope unchanged; intercept {{{ -7/6-47/6=-54/6=-9 }}}
{{{ y=(8/6)*x - 9 }}}
removing fractions:
6y=8x-54 or 4x-27=3y

Check (6,-1) 24-27=-3
Graphically:
{{{ graph(300,300,-20,20,-20,20,y=(8x-7)/6,y=(4x-27)/3) }}}