Find the equation of the line passing through the origin and perpendicular to the line y + 5x = 3.

Converting y + 5x = 3 in the form y = mx + c we get,

⇒ y = -5x + 3

Comparing above equation with y = mx + c we get, m = -5

For two lines to be perpendicular, the product of their gradients must be -1.

Let slope of required line be m₂, then :

⇒ -5 × m₂ = -1

⇒ m₂ = $\dfrac{-1}{-5}$

⇒ m₂ = $\dfrac{1}{5}$

Using the slope-intercept form y = mx + c. Since the line passes through the origin, the y-intercept is 0.

⇒ y = $\dfrac{1}{5}$x + 0

⇒ 5y = x

⇒ x - 5y = 0.

Hence, the equation of the required line is x - 5y = 0.