ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10

In this question a straight line having a point and makes positive equal intercepts on axes.

You have to find the equation of the straight line.

This is the Question Number 28, Exercise 12.1 of M.L Aggarwal.

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# Find the equation of the straight line containing the point (3, 2) and making positive equal intercepts on axes.

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Let the line containing the point P (3, 2) pass through x-axis at A (x, 0) and y-axis at B (0, y)

Given, OA = OB

Thus, x = y

Now, the slope of the line (m) = y

_{2}– y_{1}/ x_{2}– x_{1}= 0 – y/ x – 0

= -x/x = -1

Hence, the equation of the line will be

y – y

_{1}= m (x – x_{1})y – 2 = -1 (x – 3)

y – 2 = -x + 3

⇒ x + y – 5 = 0