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Question
Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.
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Solution
\[\text { Here, } m = \tan {45}^\circ = 1\]
\[ x_1 = - 2 \text { and } y_1 = 3\]
Substituting these values in \[y - y_1 = m\left( x - x_1 \right)\], we get:
\[y - 3 = 1\left( x + 2 \right)\]
\[ \Rightarrow y - 3 = x + 2\]
\[ \Rightarrow x - y + 5 = 0\]
Hence, the equation of the required line is \[x - y + 5 = 0\]
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