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Mathematics

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

  1. equal

  2. having same sign

  3. equal in magnitude with opposite signs

  4. not equal

Straight Line Eq

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Answer

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 = y2y1x2x1\dfrac{y2 - y1}{x2 - x1}

From figure,

The inclination of a line, which is not passing through origin, is 1. Its intercept with both the axes are : Equation of a Line, Concise Mathematics Solutions ICSE Class 10.

Slope of DE = Slope of AB = 1

Substituting values we get :

Slope of DE=b00a1=bab=a.\Rightarrow \text{Slope of DE} = \dfrac{b - 0}{0 - a} \\[1em] \Rightarrow 1 = \dfrac{b}{-a} \\[1em] \Rightarrow b = -a.

From figure,

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

Hence, Option 3 is the correct option.

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