16. This exercise makes use of graphing transformations. (See Chapter 1, Section 1.3.) (a) Starting with the graph of y = x, suppose that the graph is stretched vertically by a factor of m. What is the equation of the new line? (b) Starting with the graph of y = x, suppose that the graph is shifted vertically by the amount b. What is the equation of the new line?
(c) Starting with the graph of y = x, suppose that the graph is stretched vertically by a factor of m and then shifted vertically by the amount b. What is the equation of the new line?
(d) Starting with the graph of y = x, suppose that the graph is shifted vertically by the amount b and then stretched vertically by the factor m. What is the equation of the new line?
(e) By what amount must the graph of y = mx be shifted horizontally to produce the line with equation y = mx + b? (f) By what angle must the horizontal line with equation y = 0 be rotated to obtain the line with equation y mx?