The point of intersection of the graph of $N(t)=2t+3$ with the graph of $M(t)=-5t+7$ can be determined as follows:
$$\begin{align}
2t+3=-5t+7 & \Leftrightarrow 7t+3 =7\\
& \Leftrightarrow 7t=4\\
& \Leftrightarrow t=\frac{4}{7},
\end{align}$$
and $N(\frac{4}{7})=2\cdot \frac{4}{7}+3=4\frac{1}{7}$. Hence, the point of intersection is $(\frac{4}{7},4\frac{1}{7})$. You might check your answer, indeed: $M(\frac{4}{7})=4\frac{1}{7}$.
