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.

Answer 1

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

\[y - 5 = 1\left( x - 0 \right) \text { and } y - 5 = - 1\left( x - 0 \right)\]

\[ \Rightarrow y - x - 5 =\text {  and } y + x - 5 = 0\]

\[ \Rightarrow y = x + 5 \text { and }x + y = 5\]