Find the equation of the line that is tangent to both of the parabolas $y^2 = 4x$ and $x^2 = -32y.$  Enter your answer in the form "$y = mx + b$".
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the equation of the line that is tangent to both of the parabolas $y^2 = 4x$ and $x^2 = -32y.$  Enter your answer in the form "$y = mx + b$".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
y = \frac{1}{2} x + 2
Find the equation of the line that is tangent to both of the parabolas $y^2 = 4x$ and $x^2 = -32y.$  Enter your answer in the form "$y = mx + b$".
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