Consider the linear inequality 3x+4y<0.
a. (i) Define the term "boundary line" for a linear inequality in two variables.
b. (ii) The boundary line of the given inequality passes through the origin. Explain, with reason, why the origin cannot be used as a test point to locate the solution half-plane. Choose another convenient test point and justify your choice.
c. (iii) Describe, step by step, how you would decide which half-plane to shade for the given inequality once the test point is selected.