The line joining the points $(2,-3)$, $(-5,1)$ and  $(7,-1)$, $(0,3)$ are

 

The given points are $(2,-3)$ and $(-5,1)$ and also $(\dot{7},-1)$ and $(0,3)$.

The formula for slope of the line joining two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is  $m=\frac{y_2-y_1}{x_2-x_1}$.

Slope of the line joining the points $(2,-3)$ and $(-5,1)$ is given by

$$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ {m}_1=\frac{1-\left(-3\right)}{-5-2} \\ {m}_1=-\frac{4}{7} \end{gathered}$$

Slope of the line joining the points  $\left(7,-1\right)$ and $\left(0,3\right)$ is given by 

$$\begin{gathered} m_2=\frac{y_2-y_1}{x_2-x_1} \\ {m}_2=\frac{3-\left(-1\right)}{0-7} \\ {m}_2=-\frac{4}{7} \end{gathered}$$

The slope the line joining the points are equal. That is, $m_1=m_2$

Therefore, the two lines are parallel.

Hence, option $\left(1\right)$ is the correct answer.