Given the line:
[tex]6y-5x=9[/tex]You need to remember the Slope-Intercept Form of the equation of a line:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
In order to write the given equation in Slope-Intercept Form, you have to solve for "y":
[tex]\begin{gathered} 6y=5x+9 \\ \\ y=\frac{5}{6}x+\frac{9}{6} \\ \\ y=\frac{5}{6}x+\frac{3}{2} \end{gathered}[/tex]Notice that:
[tex]m=\frac{5}{6}[/tex]By definition, the slopes of parallel lines are equal. Therefore, the slope of a line parallel to the given must be:
[tex]m=\frac{5}{6}[/tex]Hence, the answer is:
[tex]m=\frac{5}{6}[/tex]