Show that two lines `a_1x+b_1y+c_1=0`and `a_2x+b_2y+c_2=0`, where `b_1,b_2!=0`are :
(i) Parallel if `(a_1)/(b_1)=(a_2)/(b_2),`and (ii) perpendicular if `a_1a_2+b_1b_2=0`.

Explanation

To show that the two lines given by the equations \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) are parallel or perpendicular under the specified conditions, we will follow these steps:

### Step 1: Convert the equations to slope-intercept form
We start by rearranging both equations into the form \( y = mx + c \).

1. For the first line \( a_1x + b_1y + c_1 = 0 \):
\[
b_1y = -a_1x - c_1 \implies y = -\frac{a_1}{b_1}x - \frac{c_1}{b_1}
...