First, we need to find the slope of the given line to which our unknown line is parallel. Remember, parallel lines have equal slopes!
[tex]\begin{gathered} 3x-2y-7=0 \\ \\ -2y=-3x+7 \\ \\ y=\frac{3}{2}x-\frac{7}{2} \end{gathered}[/tex]By writing the equation in slope-intercept form, we find the slope to be 3/2. We will use this and the given point (-5, 9) to solve the equation of the unknown line.
So, the equation of the line in point-slope form is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-9=\frac{3}{2}(x+5) \end{gathered}[/tex]In general form, the equation is:
[tex]\begin{gathered} y-9=\frac{3}{2}(x+5) \\ \\ 2y-18=3(x+5) \\ 2y-18=3x+15 \\ -3x+2y-33=0 \\ 3x-2y+33=0 \end{gathered}[/tex]