First let's find the slope of the given line
[tex]\begin{gathered} 4x+5y=6 \\ 5y=-4x+6 \\ y=\frac{-4}{5}x+6 \\ so\text{ by slope intercept form , slope of given line is }\frac{-4}{5} \end{gathered}[/tex]Since the rerquired line is parallel to the given line so its slope will also be -4/5 as slope of two parallel lines is same.
Now let's find the equation of the required line by point-slope form :-
[tex]\begin{gathered} y-(-3)=\frac{-4}{5}(x-(-1)) \\ y+3=\frac{-4}{5}((x+1)) \\ 5y+15=-4x-4 \\ 4x+5y=-19 \end{gathered}[/tex]So the equation of the requird line is 4x+5y=-19
