A variable straight line is represented by the equation px−6y+18=0, where p is a real parameter.
a. (i) Obtain expressions for the slope, the x-intercept, and the y-intercept of the line in terms of p.
b. (ii) The triangle bounded by the line and the coordinate axes is required to have a constant area of 18 square units. Derive the quadratic equation that p must satisfy.
c. (iii) Solve the quadratic equation obtained in part (ii) and hence write the two possible equations of the line that meet the given area condition.