Question

The inclination of a line, which is not passing through origin, is 1. Its intercepts with both the axes are ______.

Options

• equal

• having same sign

• equal in magnitude with opposite signs

• not equal

Answer 1

The inclination of a line, which is not passing through origin, is 1. Its intercepts with both the axes are having same sign.

Explanation:

Let AB be the line not passing through the origin and intersecting x-axis at D and y-axis at E.

We know that,

y-coordinate = 0 at x axis and x-coordinate = 0 at y-axis.

Let D = (a, 0) and E = (0, b).

By formula,

Slope = `​(y_2​ − y_1)/(x_2​ − x_1)​​`

From figure,

Slope of DE = Slope of AB = 1

Substituting values we get:

⇒Slope of DE = (b−0)/(0−a)

⇒ 1 = `b /(−a)`

⇒ b = −a.

From figure,

a and b are intercepts on x-axis and y-axis respectively.