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.

To determine the slope of the tangent line at point Q on circle P, we need to remember that the tangent line at any point on a circle is perpendicular to the radius extending to that point. The given equation of the diameter is y = 4x + 2, which has a slope of 4.

The slope of the radius to point Q is 4, so the slope of the tangent line, being perpendicular, will be the negative reciprocal of 4, which is -1/4.

Therefore, the correct statement is D: The slope of the tangent line is -1/4.