Answer
$$L = 7\sqrt 5 $$
Work Step by Step
$$\eqalign{
& x = 2y - 4,{\text{ for }} - 3 \leqslant y \leqslant 4 \cr
& {\text{Calculate the Arc Length }} \cr
& \frac{{dx}}{{dy}} = \frac{d}{{dy}}\left[ {2y - 4} \right] \cr
& \frac{{dx}}{{dy}} = 2 \cr
& {\text{Use the formula }}L = \int_c^d {\sqrt {1 + {{\left( {\frac{{dx}}{{dy}}} \right)}^2}} dy} \cr
& L = \int_{ - 3}^4 {\sqrt {1 + {{\left( 2 \right)}^2}} dy} \cr
& L = \int_{ - 3}^4 {\sqrt {1 + 4} dy} \cr
& L = \int_{ - 3}^4 {\sqrt 5 dy} \cr
& {\text{Integrating}} \cr
& L = \sqrt 5 \left[ y \right]_{ - 3}^4 \cr
& L = \sqrt 5 \left( {4 - \left( { - 3} \right)} \right) \cr
& L = 7\sqrt 5 \cr} $$
