Answer
The lines are not parallel.
Work Step by Step
For line $a$
$(x_1,y_1)=(-5,3)$ and $(x_2,y_2)=(-6,-1)$.
Use slope formula.
$\Rightarrow m=\frac{y_2−y_1}{x_2−x_1}$
Substitute all the values.
$\Rightarrow m_1=\frac{-1−3}{-6−(-5)}$
Simplify.
$\Rightarrow m_1=\frac{-4}{-6+5}$
$\Rightarrow m_1=\frac{-4}{-1}$
$\Rightarrow m_1=\frac{4}{1}$
For line $b$
$(x_1,y_1)=(3,-2)$ and $(x_2,y_2)=(2,-7)$.
Use slope formula.
$\Rightarrow m=\frac{y_2−y_1}{x_2−x_1}$
Substitute all the values.
$\Rightarrow m_2=\frac{-7−(-2)}{2−3}$
Simplify.
$\Rightarrow m_2=\frac{-7+2}{-1}$
$\Rightarrow m_2=\frac{-5}{-1}$
$\Rightarrow m_2=\frac{5}{1}$
$m_1\neq m_2$
Hence, the lines are not parallel.
