When circle P is plotted on a coordinate plane, the equation of the diameter that passes through point Q on the circle is y=4 x+2. Which statement describes the equation of a line that is tangent to circle P at point Q? A. The slope of the tangent line is -4. B. The slope of the tangent line is 1/4. C. The slope of the tangent line is 4. D. The slope of the tangent line is -1/4.

1. Since the diameter passing through point \( Q \) has the equation \[ y = 4x + 2, \] its slope is \( 4 \). 2. The radius drawn from the center of circle \( P \) to \( Q \) lies along this diameter, so the slope of the radius is also \( 4 \). 3. The tangent line at \( Q \) to the circle is perpendicular to the radius at \( Q \). Therefore, its slope is the negative reciprocal of \( 4 \). 4. The negative reciprocal of \( 4 \) is computed as: \[ -\frac{1}{4}. \] 5. Thus, the equation of the line tangent to the circle at \( Q \) has a slope of \( -\frac{1}{4} \), which corresponds to option D.