Let's solve the given equation step-by-step to find the equivalent equation for the line [tex]\( y - 6 = -4(x + 1) \)[/tex].
1. Distribute the -4 on the right-hand side:
[tex]\( y - 6 = -4(x + 1) \)[/tex]
Distributing the [tex]\(-4\)[/tex]:
[tex]\[ y - 6 = -4x - 4 \][/tex]
2. Add 6 to both sides to isolate [tex]\( y \)[/tex]:
[tex]\[ y - 6 + 6 = -4x - 4 + 6 \][/tex]
Simplifying this:
[tex]\[ y = -4x - 4 + 6 \][/tex]
[tex]\[ y = -4x + 2 \][/tex]
The equation of the line in slope-intercept form [tex]\( y = mx + b \)[/tex] is now [tex]\( y = -4x + 2 \)[/tex].
Comparing this with the options given:
A. [tex]\( y = -4x - 4 \)[/tex]
B. [tex]\( y = -4x + 3 \)[/tex]
C. [tex]\( y = -4x + 7 \)[/tex]
D. [tex]\( y = -4x + 2 \)[/tex]
The correct answer is [tex]\( \boxed{D} \)[/tex], which is [tex]\( y = -4x + 2 \)[/tex].
