Points A(1,2) and B(4,8) lie on a railway track represented by a straight line. A second track is to be laid parallel to the first one and must pass through the point C(5,−1).
(i) Determine the slope of the track AB and write its equation in the form y=mx+c.
(ii) Obtain the equation of the track through C that is parallel to AB.
(iii) Find the coordinates of the point D where the new track meets the x-axis.
(iv) Calculate the acute angle of inclination of both tracks with the positive direction of the x-axis. (Give your answer correct to the nearest degree.)