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