A line perpendicular to another line or to a tangent line is often called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curves at the given point P.
y = 2/x; P(1, 2)

Verified step by step guidance

1. Step 1: Find the derivative of the function y = \frac{2}{x} to determine the slope of the tangent line at point P(1, 2). The derivative, y', can be found using the power rule and the fact that \frac{d}{dx}(x^{-1}) = -x^{-2}.
2. Step 2: Evaluate the derivative at x = 1 to find the slope of the tangent line at point P(1, 2). Substitute x = 1 into the derivative to get the slope of the tangent line.
3. Step 3: Determine the slope of the line perpendicular to the tangent line. The slope of the normal line is the negative reciprocal of the slope of the tangent line.
4. Step 4: Use the point-slope form of a line equation, y - y_1 = m(x - x_1), where m is the slope of the normal line and (x_1, y_1) is the point P(1, 2), to write the equation of the normal line.
5. Step 5: Simplify the equation from Step 4 to get the final equation of the normal line in slope-intercept form, y = mx + b, or any other preferred form.