Given: A line which is parallel to
![\[x-axis\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-10f8e73a8537bcb6a398489836795e56_l3.png "Rendered by QuickLaTeX.com")
and passing through
![\[\left( 3,-\text{ }5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e16dc3167e030a98277f36ea42de7b78_l3.png "Rendered by QuickLaTeX.com")
By using the formula,
The equation of line:
![\[[y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6f261d78df80f708cbcd73a94df3c69c_l3.png "Rendered by QuickLaTeX.com")
We know that the parallel lines have equal slopes
And, the slope of
is always
![\[0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b4f4fbf425b3e7b1e844d7922169d13c_l3.png "Rendered by QuickLaTeX.com")
Then
The slope of line,
![\[m\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7aa7b649adc2b0fa69d195aefe94650c_l3.png "Rendered by QuickLaTeX.com")
Coordinates of line are
![\[({{x}_{1}},\text{ }{{y}_{1}})\text{ }=\text{ }\left( 3,-\text{ }5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e0043eb391b28b411bb27600041d3384_l3.png "Rendered by QuickLaTeX.com")
The equation of line
![\[=\text{ }y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8bba50ff13e1ce70ceae3a5868ff264e_l3.png "Rendered by QuickLaTeX.com")
Now, substitute the values, we get
![\[y\text{ }-\text{ }\left( -\text{ }5 \right)\text{ }=\text{ }0\left( x\text{ }-\text{ }3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5c9f1d75880254150b621fee85e31b0b_l3.png "Rendered by QuickLaTeX.com")
![\[y\text{ }+\text{ }5\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c229f94489feabfe603d7a339b313b06_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line is