ANSWER
[tex]y = \frac{3}{2} x + 8[/tex]
EXPLANATION
The line given to us has equation,
[tex]2x + 3y = 9[/tex]
We need to write this equation in the slope intercept form to obtain,
[tex]3y = - 2x + 9[/tex]
[tex]\Rightarrow \: y = - \frac{2}{3}x + 3 [/tex]
The slope of this line is
[tex]m_1 = - \frac{2}{3} [/tex]
Let the slope of the perpendicular line be
[tex]m_2[/tex]
Then
[tex]m_1 \times m_2 = - 1[/tex]
[tex] - \frac{2}{3} m_2= - 1[/tex]
This implies that,
[tex]m_2 = - 1 \times - \frac{3}{2} [/tex]
[tex]m_2 = \frac{3}{2} [/tex]
Let the equation of the perpendicular line be,
[tex]y = mx + b[/tex]
We substitute the slope to get,
[tex]y = \frac{3}{2} x + b[/tex]
Since this line passes through
[tex](-2,5)[/tex]
it must satisfy its equation.
This means that,
[tex]5= \frac{3}{2} ( - 2)+ b[/tex]
[tex]5 = - 3 + b[/tex]
[tex]5 + 3 = b[/tex]
[tex]b = 8[/tex]
Wherefore the slope-intercept form is
[tex]y = \frac{3}{2} x + 8[/tex]
