Answer
$$\Delta y = 8\Delta x{\text{ }}\,\,\,{\text{and}}\,\,\,{\text{ }}dy = 8dx$$
Work Step by Step
$$\eqalign{
& {\text{Let }}y = 8x - 4 \cr
& \cr
& {\text{Calculating }}\Delta y.\,\,\,f\left( x \right) = 8x - 4 \cr
& \Delta y = f\left( {x + \Delta x} \right) - f\left( x \right) \cr
& {\text{Then evaluating }} \cr
& \Delta y = 8\left( {x + \Delta x} \right) - 4 - \left( {8x - 4} \right) \cr
& \Delta y = 8x + 8\Delta x - 4 - 8x + 4 \cr
& {\text{Simplifying}} \cr
& \Delta y = 8\Delta x \cr
& \cr
& {\text{and}} \cr
& y = 8x - 4 \cr
& \frac{{dy}}{{dx}} = 8,{\text{ so }}dy = 8dx \cr
& \cr
& \Delta y = 8\Delta x{\text{ }}\,\,\,{\text{and}}\,\,\,{\text{ }}dy = 8dx \cr} $$
