**Two lines, a**_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0

If \(\frac{a_1}{a_2}\)=\(\frac{b_1}{b_2}\)=\(\frac{c_1}{c_2}\), then the lines coincide

If \(\frac{a_1}{a_2}\)= \(\frac{b_1}{b_2}\)≠\(\frac{c_1}{c_2}\), then the lines are parallel

If \(\frac{a_1}{a_2}\)≠ \(\frac{b_1}{b_2}\)≠\(\frac{c_1}{c_2}\), then the lines intersect

**Given line 2x + 3y - 8 = 0**

**(i) intersecting line:**

3x + 2y – 6 = 0

**(ii) parallel line:**

4x + 6y = 15

**(iii) coincident line:**

4x + 6y – 16 = 0