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Question
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is ______.
Options
5y – 3x + 15 = 0
3y – 5x + 15 = 0
5y – 3x – 15 = 0
None of these
Solution
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is 5y – 3x + 15 = 0.
Explanation:
Since the lines cut off intercepts – 3 on y-axis then the line is passing through the point (0, – 3).
Given that: tan θ = `3/5`
⇒ Slope of the line m = `3/5`
So, the equation of the line is y – y1 = m(x – x1)
⇒ y + 3 = `3/5(x - 0)`
⇒ 5y + 15 = 3x
⇒ 3x – 5y – 15 = 0
⇒ 5y – 3x + 15 = 0
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