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Question
Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
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Solution
It is given that the lines are equally inclined to the axes.
So, their inclinations with the positive x-axis are \[{45}^\circ \text { and } {135}^\circ\].
Let \[m_1 \text { and } m_2\] be the slopes of the lines.
\[\therefore m_1 = \tan {45}^\circ = 1 \text { and } m_2 = \tan {135}^\circ = - \tan {45}^\circ = - 1\]
Thus, the equations of the lines passing through (0, 5) with slopes \[1 \text { and }- 1\] are
\[y - 5 = 1\left( x - 0 \right) \text { and } y - 5 = - 1\left( x - 0 \right)\]
\[ \Rightarrow y - x - 5 =\text { and } y + x - 5 = 0\]
\[ \Rightarrow y = x + 5 \text { and }x + y = 5\]
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