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