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

Answer 1

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