Let m be a real number. In the rectangular coordinate plane,
the slope of a line passing through the point $( 0,1 )$ is $m$,
the slope of a line passing through the point $( 0,0 )$ is $2 m$,
the slope of a line passing through the point $( 1,0 )$ is $3 m$, and these three lines intersect at one point.
Accordingly, what is the value of $m$? A) $\frac { 1 } { 2 }$ B) $\frac { 1 } { 3 }$ C) $\frac { 3 } { 4 }$ D) $\frac { 3 } { 5 }$ E) $\frac { 4 } { 5 }$
Let m be a real number. In the rectangular coordinate plane,
\begin{itemize}
\item the slope of a line passing through the point $( 0,1 )$ is $m$,
\item the slope of a line passing through the point $( 0,0 )$ is $2 m$,
\item the slope of a line passing through the point $( 1,0 )$ is $3 m$, and these three lines intersect at one point.
\end{itemize}
Accordingly, what is the value of $m$?\\
A) $\frac { 1 } { 2 }$\\
B) $\frac { 1 } { 3 }$\\
C) $\frac { 3 } { 4 }$\\
D) $\frac { 3 } { 5 }$\\
E) $\frac { 4 } { 5 }$