equation of line

5x + 6y = 11 

6y = -5x + 11

y = $-\frac{5}{6} x + \frac{11}{6}$

 

Since the slope is $-\frac{5}{6}$ , the perpendicular slope to it is $\frac{6}{5}$
 

y = mx + b  --> (15, -7)

$-7 = \frac{6}{5}(15) + b$

 $-7 = 18 + b$

$b = -25$

 

This means the equation of this line is:
$y = \frac{6}{5}x - 25$