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Question
Find the equation of the straight line which passes through (1, −2) and cuts off equal intercepts on the axes.
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Solution
The equation of the line cutting off equal intercepts 'a' on the coordinate is
\[\frac{x}{a} + \frac{y}{b} = 1\]
\[ \Rightarrow \frac{x}{a} + \frac{y}{a} = 1\]
\[ \Rightarrow x + y = a\]
The line x + y = a passes through (1, −2)
\[\therefore 1 - 2 = a\]
\[ \Rightarrow a = - 1\]
Hence, the equation of the line is \[x + y = - 1\]
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