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Question
Find the equation of the line that has x-intercept = –3 and is perpendicular to 3x + 5y = 1.
Solution
x-intercept of the line = –3
∴ Required line passes through (–3, 0) and is perpendicular to the line
3x + 5y = 1
5y = 1 – 3x
= –3x + 1
`y = -3/5 x + 1/5`
∴ Slope `m = -3/5`
Slope of the line perpendicular to the given line = `(+5)/3`
∴ Equation of the required line through = (–3, 0) and having slope `5/3` is given by
`y - 0 = 5/3(x + 3)`
`\implies` 3y = 5x + 15
`\implies` 5x – 3y + 15 = 0
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