Study the inequality 5x−10y≥0 and represent its solution set on the Cartesian plane.
a. (i) Reduce the inequality to its simplest form and write the corresponding boundary line.
b. (ii) Draw the boundary line on graph paper, marking its intercepts clearly.
c. (iii) Since the origin lies on the boundary, select a different integer test point and explain why it is suitable.
d. (iv) Decide which half-plane contains the solutions, shade it appropriately, and verify whether the point (3,1) is included in the solution set.