Final answer:
The graph of y = 4csc(θ - π/4) represents a D) line.
Step-by-step explanation:
The given function is y = 4csc(θ - π/4). The trigonometric function csc is the reciprocal of sine, so we can rewrite the function as y = 4/sin(θ - π/4). The graph of y = 4csc(θ - π/4) is a line.
This is because the reciprocal of sine can be thought of as the ratio of the length of the hypotenuse to the length of the side opposite the angle in a right triangle.
Since the length of the hypotenuse and the side opposite are always positive, the value of the reciprocal is always positive and the graph is a line.