Question

Classify the following pair of line as coincident, parallel or intersecting:

x − y = 0 and 3x − 3y + 5 = 0]

Answer 1

Let \[a_1 x + b_1 y + c_1 = 0 \text { and } a_2 x + b_2 y + c_2 = 0\]

(a) The lines intersect if \[\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\] is true.

(b) The lines are parallel if \[\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\] is true.

(c) The lines are coincident if \[\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\] is true.

 x − y = 0 and 3x − 3y + 5 = 0

Here, 

\[\frac{1}{3} = \frac{- 1}{- 3} \neq \frac{0}{5}\]

Therefore, the lines x − y = 0 and 3x − 3y + 5 = 0 are parallel.