ANSWER
[tex]y = \frac{3}{2} x + 8[/tex]
EXPLANATION
The line given to us has equation,
[tex]2x + 3y = 9.[/tex]
Let us rewrite in slope intercept form to get,
[tex]3y = - 2x + 9[/tex]
[tex]\Rightarrow \: y = - \frac{2}{3}x + 3[/tex]
When we compare to
[tex]y = mx + b[/tex]
We can see that, the slope
[tex] m_1 =- \frac{2}{3} [/tex]
The slope of the line that is perpendicular this line can be obtained using the relation,
[tex]m_1\times m_2=-1[/tex]
Thus,
[tex] - \frac{2}{3} \times m_2 = -1[/tex]
[tex] m_2 = -1 \times - \frac{3}{2} = \frac{3}{2} [/tex]
Hence the line in slope intercept form becomes,
[tex]y = \frac{3}{2} x + b[/tex]
Since this line passes through
[tex](-2,5)[/tex]
, we substitute it to find the value of
[tex]b.[/tex]
[tex]5= \frac{3}{2} ( - 2)+ b[/tex]
[tex]5= - 3+ b[/tex]
[tex]b = 5 + 3[/tex]
[tex]b = 8[/tex]
Hence the slope-intercept form is
[tex]y = \frac{3}{2} x + 8[/tex]
