Chapter 8 - Polar Coordinates; Vectors - Section 8.2 Polar Equations and Graphs - 8.2 Assess Your Understanding - Page 606: 30

$\bf{Graph-A}$

Here $\theta=\dfrac{\pi}{4}$ implies that we have an angle of $\dfrac{\pi}{4}$ ($45^{\circ}$) with no specified radius. This results in a diagonal line with positive slope. The only graph that matches this description is A. Therefore, our required answer is $\bf{Graph-A}$.