Find the Constant a Such That the Function $f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.$

Multiple Choice

Find the constant a such that the function $f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.$
is continuous on the entire real line.

A) $a = 2 , b = 0$
B) $a = 2 , b = - 4$
C) $a = - 2 , b = - 4$
D) $a = - 2 , b = 4$
E) $a = 2 , b = 4$