product of two perpendicular line slopes must equals - 1 ;
As you know the coefficient of x is the slope of the line
Thus if we suppose that line has a slope of m , we have :
m × 2 = - 1
m = - 1 / 2
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y = ax + b
y = - 1 / 2 x + b
The line passes through the point ( - 2 , - 2 ) thus :
- 2 = - 1 /2 × ( - 2 ) + b
- 2 = 1 + b
b = - 3
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y = - 1/2 x - 3
Which mean the option c is the correct answer.