A2. Of the two drawn lines in the coordinate system, one of the lines has the equation $y=a x+b$ for some different real numbers $a$ and $b$ (see figure). Which of the following equations could be the equation of the other line?
(A) $y=a x-b$
(B) $y=b x+a$
(C) $y=\frac{b}{a} x+b$
(D) $y=-b x+a$
(E) $y=\frac{a}{b} x+a$
A2. For both drawn lines, it holds that they have a slope coefficient greater than zero and an initial value greater than zero. Therefore, $a>0$ and $b>0$, and the equation of the second line cannot be either $y=a x-b$ or $y=-b x+a$. Since the initial values for the drawn lines are different, the equation of the second line cannot be equal to $y=\frac{b}{a} x+b$. Thus, only the equations $y=b x+a$ and $y=\frac{a}{b} x+a$ remain. If $b>a$, then the initial value of the second line is smaller than the initial value of the first line, so the slope of the second line must also be smaller than the slope of the first line, which is $a$. In this case, the possible equation of the second line is only $y=\frac{a}{b} x+a$. If, however, $b<a$, the initial value of the second line is greater than the initial value of the first line, and the slope of the second line must also be greater than the slope of the first line, which is $a$. Therefore, in this case, the possible equation of the second line is also only $y=\frac{a}{b} x+a$.