For a straight line in the Cartesian plane, answer the following:
(i) Write the equation of the line when its slope is m and it passes through a fixed point (x1,y1). Express the answer in the appropriate form.
(ii) Rewrite the same equation obtained in part (i) so that y is expressed explicitly in terms of x. Hence, show that the constant term can be written as c=y1−mx1.
(iii) Give a brief geometrical explanation of why specifying one point on the plane together with the slope is sufficient to determine a unique straight line.