With slope \[-\text{ }2\]and intersecting the x–axis at a distance of \[3\]units to the left of origin
The slope is \[-\text{ }2\] and the coordinates are \[\left( -\text{ }3,\text{ }0 \right)\]
Now, the required equation of line is \[y\text{ }-\text{ }{{y}_{1}}~=\text{ }m\text{ }(x\text{ }-\text{ }{{x}_{1}})\]
Substitute the values, we get
\[y\text{ }-\text{ }0\text{ }=\text{ }-\text{ }2\left( x\text{ }+\text{ }3 \right)\]
\[y\text{ }=\text{ }-\text{ }2x\text{ }-\text{ }6\]
So,
\[2x\text{ }+\text{ }y\text{ }+\text{ }6\text{ }=\text{ }0\]