Question

Find the equation of the line passing through (−2, 1) and perpendicular to 4x + 5y = 6.

Answer 1

4x + 5y = 6

5y = −4x + 6

`y = (-4x)/5 + 6/5`

Slope of this line = `(-4)/5`

The required line is perpendicular to the line 4x + 5y = 6.

∴ Slope of the required line = `(-1 )/"slope of the given line"` 

= `(-1)/((-4)/5)`

= `5/4`

The required equation of the line is given by

y − y₁ = m(x − x₁)

`y − 1 = 5/4 (x + 2)`

4y − 4 = 5x + 10

5x − 4y + 10 + 4 = 0

5x − 4y + 14 = 0