To rewrite the equation [tex]\( y - 8 = 2(x + 4) \)[/tex] into slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[ y - 8 = 2(x + 4) \][/tex]
2. Expand the right-hand side:
[tex]\[ y - 8 = 2 \cdot x + 2 \cdot 4 \][/tex]
[tex]\[ y - 8 = 2x + 8 \][/tex]
3. Isolate [tex]\( y \)[/tex] on the left side to put the equation in the form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = 2x + 8 + 8 \][/tex]
[tex]\[ y = 2x + 16 \][/tex]
The simplified form of the equation is:
[tex]\[ y = 2x + 16 \][/tex]
This equation is now in the slope-intercept form [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Hence, the best answer is:
[tex]\[ \boxed{D. \; y = 2x + 16} \][/tex]
