Question

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

Answer 1

The given line is $$y + 5x = 3 \implies y = -5x + 3$$. 

Slope $$m_1 = -5$$.

The perpendicular line has slope:

$$m = -\frac{1}{m_1}$$

$$= -\frac{1}{-5}$$

$$= \frac{1}{5}$$

Passing through origin $$(0, 0)$$: 

$$y - 0 = \frac{1}{5}(x - 0)$$

$$5y = x$$

$$x - 5y = 0$$