Answer:
[tex]\sf D.\quad \textsf{The slope of the tangent line is }-\dfrac{1}{4}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]\sf y=mx+b[/tex]
(where m is the slope and b is the y-intercept).
The equation of the diameter is [tex]\sf y=4x+2[/tex], therefore its slope is 4.
The tangent of a circle is always perpendicular to the radius, which means it is also perpendicular to the diameter.
If two lines are perpendicular to each other, the product of their slopes is -1.
[tex]\begin{aligned}\textsf{slope of diameter} \times \textsf{slope of tangent} & =-1\\\implies 4 \times \textsf{slope of tangent} & =-1\\\implies \textsf{slope of tangent} & = -\dfrac{1}{4}\end{aligned}[/tex]
Therefore, the slope of the tangent line is [tex]\sf -\dfrac{1}{4}[/tex]
