ANSWER
[tex]y=-\frac{9}{2}x-\frac{5}{2}[/tex]EXPLANATION
Two lines are perpendicular if their slopes are opposite reciprocals of each other.
In this case, we can rewrite the equation of the given line in slope-intercept form by solving the equation for y,
[tex]2x-9y=-3[/tex]Add 9y to both sides,
[tex]\begin{gathered} 2x-9y+9y=-3+9y \\ 2x=-3+9y \end{gathered}[/tex]Add 3 to both sides,
[tex]2x+3=9y[/tex]And divide both sides by 9,
[tex]y=\frac{2}{9}x+\frac{3}{9}[/tex]As we can see, the slope of the given line is 2/9. Its opposite reciprocal is -9/2. This is the slope of the line we have to find,
[tex]y=-\frac{9}{2}x+b[/tex]To find the y-intercept, b, we have to use the point (-1, 2). Replace x and y with the coordinates of the point,
[tex]2=-\frac{9}{2}(-1)+b[/tex]And solve for b,
[tex]\begin{gathered} 2=\frac{9}{2}+b \\ \\ 2-\frac{9}{2}=b \\ \\ \frac{4-9}{2}=b \\ \\ -\frac{5}{2}=b \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-\frac{9}{2}x-\frac{5}{2}[/tex]