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

$\text{It is given that the lines are equally inclined to the axes.}\text{So, their inclinations with the positive x-axis are}{45}^{\circ }and{135}^{\circ }$

$Let{m}_{1}and{m}_2\text{be the slopes of the lines.}\therefore m_1=tan{45}^{\circ }=1and{m}_2=tan{135}^{\circ }=tan{45}^{\circ }=-1\text{Thus, the equations of the lines passing through (0, 5) with slopes 1 and -1 are}y-5=1(x-0)andy-5=-1(x-0)\Rightarrow y-x-5=andy+x-5=0\Rightarrow y=x+5andx+y=5$