Clear y from both equations to find the slope y intercept form of the equations
[tex]\begin{gathered} 4x-9y=-5 \\ -9y=-4x-5 \\ y=\frac{-4x-5}{-9} \\ y=\frac{4}{9}x+\frac{5}{9}\text{ (Eq. 1)} \\ -x-4y=-2 \\ -4y=x-2 \\ y=\frac{x-2}{-4} \\ y=-\frac{x}{4}+\frac{1}{2}\text{ (Eq. 2)} \end{gathered}[/tex]Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2
[tex]\begin{gathered} m1\cdot m3=-1 \\ m3=-\frac{1}{m1} \\ m3=-\frac{1}{\frac{4}{9}} \\ m3=-\frac{9}{4} \\ y=-\frac{9}{4}x+\frac{1}{2}\text{ (Eq. 3)} \end{gathered}[/tex]Eq. 3 is the equation for the line
