Is the line x – 3y = 4 perpendicular to the line 3x – y = 7?

Given lines,

⇒ x - 3y = 4 and 3x - y = 7

⇒ 3y = x - 4 and y = 3x - 7

⇒ y = $\dfrac{1}{3}x - \dfrac{4}{3}$ and y = 3x - 7

Comparing above equations with y = mx + c we get,

Slope of 1st line = $\dfrac{1}{3}$

Slope of 2nd line = 3

Since,

Slope of 1st line × Slope of 2nd line = $\dfrac{1}{3} \times 3 = 1$ which is not equal to -1.

Hence, the lines x - 3y = 4 and 3x - y = 7 are not perpendicular to each other.