Consider two points A and B in the Cartesian plane.
a. (i) Define the slope of the straight line passing through A(x1, y1) and B(x2, y2).
b. (ii) Without calculating any exact numerical value, decide whether the slope of the line joining A(−3, 4) and B(2, 7) is positive, negative or zero. Justify your answer clearly.
c. (iii) Repeat part (ii) for the points C(−5, 2) and D(4, −1).
d. (iv) Explain, in general terms, how the relative positions of two points with respect to the axes determine the sign of the slope of the line joining them.