Answer
Yes, the provided statement makes sense -- the lines are parallel.
Work Step by Step
As per the provided statement, the slopes / rate of change are the same.
That is, ${{m}_{1}}={{m}_{2}}$.
For example, consider a linear model: $p\left( x \right)=mx+c$.
Where $m$ is the slope or rate of change. The necessary condition for the lines to be parallel is that they must have the same slope.
Consider another line $q\left( x \right)=mx+d$.
Where $m$ is the slope.
Therefore, the lines $p\left( x \right)=mx+c$ and $q\left( x \right)=mx+d$ will be parallel. So, the statement makes a sense.
