Given:

A straight line passing through the point \[\left( 0,\text{ }0 \right)\] and slope is \[m\]

By using the formula,

The equation of line is \[[y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})]\]

It is given that, the line is passing through \[\left( 0,\text{ }0 \right)\] and the slope of line, \[m\text{ }=\text{ }m\]

Coordinates of line are \[({{x}_{1}},\text{ }{{y}_{1}})\text{ }=\text{ }\left( 0,\text{ }0 \right)\]

The equation of line \[=\text{ }y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})\]

Now, substitute the values, we get

\[y\text{ }-\text{ }0\text{ }=\text{ }m\left( x\text{ }-\text{ }0 \right)\]

\[y\text{ }=\text{ }mx\]

∴ The equation of line is \[y\text{ }=\text{ }mx\]