8x+7y +7 =0, rewrite solving for y

7y= -8x-7

y = (-8/7)x -1

the slope is -8/7

the slope of the perpendicular line is the negative inverse, change the sign and flip it upside down: 7/8

the perpendicular equation is y=(7/8)x + constant

plug the point in to get the constant term

-11 = (7/8)(2) + c

-11 = 7/4 + c

c = -11 - 7/4 = -51/4

the perpendicular line is

y=(7/8)x -51/4 or

8y = 7x -102

I think your mistake was when you didn't plug in the point into the perpendicular equation

you should have gotten -11 = (7/8)(2) + constant,

you seem to have something different. you should just replace y with -11 and replace x with 2