Question

The lines represented by 4x + 3y = 9 and px – 6y + 3 = 0 are parallel. Find the value of p.

Answer 1

Writing the given lines 4x + 3y = 9

And px – 6y + 3 = 0 in the form of y = mx + c

4x + 3y = 9

`=>` 3y = −4x + 9

`y = (-4)/3x + 9/3`

`=> y = (-4)/3x + 3`   ...(i)

Here, m₁ = slope = `(-4)/3`

And px – 6y + 3 = 0

`=>` –6y = –px – 3

`y = (-p)/(-6)x - 3/(-6)`

= `p/6x + 1/2`

`=> y = p/6x + 1/2`   ...(ii)

Here, slope m₂ = `p/6`

∵ Lines are parallel

∴ Their slopes are equal i.e., m₁ = m₂

∴ `p/6 = (-4)/3`

`=>` 3p = –24

`p = (-24)/3`

p = –8