Question 831460
First, you need the change the given equation into standard form.
2x+7y=-15
7y = -2x - 15
y = (-2/7)x - 15/7
The linear equation you are finding has a form like this also y = ax + b
In order to be perpendicular, the a of this equation you are finding and the a in the given equation must multiply together and give you - 1, so you have
(-2/7)a = -1 
a = 7/2 

So now you have the a, let's plug it in and have y = (7/2)x + b
Now you have the point (-1/2,-2) on this line, -1/2 is x and -2 is y, so you plug it in 
-2 = (7/2)*(-1/2) + b 
-2 = (-7/4) + b
-2 + 7/4 = b
-1/4 = b 
TA-DAH
Your answer is y = (7/2)x - 1/4