There are two bisectors of the coordinate axes.
Their inclinations with the positive x-axis are
![\[{{45}^{o}}~and\text{ }{{135}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6783a5710b771a7e7e51aa15d5c6a229_l3.png "Rendered by QuickLaTeX.com")
The slope of the bisector is
![\[m\text{ }=\text{ }tan\text{ }{{45}^{o}}~or\text{ }m\text{ }=\text{ }tan\text{ }{{135}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a7dde5e19443ae7f251c34a0fdcead12_l3.png "Rendered by QuickLaTeX.com")
i.e.,
![\[m\text{ }=\text{ }1\text{ }or\text{ }m\text{ }=\text{ }-1,\text{ }c\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dc089aab2fd502197d1884199595acf5_l3.png "Rendered by QuickLaTeX.com")
By using the formula,
![\[y\text{ }=\text{ }mx\text{ }+\text{ }c\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7b84e507aa950093917873b19a0626b1_l3.png "Rendered by QuickLaTeX.com")
Now, substitute the values of
![\[m\text{ }and\text{ }c\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e4adca942972193afea81358ada8c860_l3.png "Rendered by QuickLaTeX.com")
we get
![\[y\text{ }=\text{ }x\text{ }+\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5c4b08e2703d6f0744bb4be0d9c21502_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }\text{ }y\text{ }=\text{ }0\text{ }or\text{ }y\text{ }=\text{ }-x\text{ }+\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-170cac8d42167c9593770f802dba111a_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }+\text{ }y\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bfa8bc0bb50baddeeae8dfa02d783e2a_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of the bisector is
![\[x~\pm ~y\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6e52d02c0bc443b5a24afd1f22bd36fb_l3.png "Rendered by QuickLaTeX.com")