For each part, consider the straight line determined by the indicated points in the Cartesian plane.
(i) State the meaning of the term "slope" of a straight line.
(ii) Without doing any explicit calculation, predict the sign (positive, negative, zero, or not defined) of the slope of the line joining the points P(–3,5) and Q(4,–2). Give a brief reason for your answer.
(iii) The points R(2,7) and S(6,15) lie on another line. Explain which of the two lines, PQ or RS, is steeper and justify your conclusion.
(iv) Calculate the exact numerical value of the slope of the line RS and interpret its meaning with respect to movement in the coordinate plane.