Consider the straight line given by the general equation ax+by+c=0 where b=0. Answer the following questions.
a. (i) State the condition on the slopes of two non-vertical lines so that they are (a) parallel, (b) perpendicular.
b. (ii) Show that every line parallel to ax+by+c=0 can be written in the form ax+by+k=0, where k is a constant. Explain your reasoning in terms of the slope.
c. (iii) For the specific line 5x−2y+9=0, write one possible equation of a line perpendicular to it and verify that the product of the slopes of the two lines equals −1.