solved
$\displaystyle 4x-5y=6$
$\displaystyle 5y=4x-6$
$\displaystyle y=\frac{4}{5}x-\frac{6}{5}$
$\displaystyle m_1=\frac{4}{5}$
$\displaystyle m_2=-\frac{5}{4}$
Equation of the line through (1, -2) is:
$\displaystyle y+2=-\frac{5}{4}(x-1)$
$\displaystyle 4y+8=-5x+5$
$\displaystyle 5x+4y+3=0$