Answer :
To convert the given equation [tex]\( y - 5 = -2(x + 4) \)[/tex] into the slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:
1. Start with the original equation:
[tex]\[ y - 5 = -2(x + 4) \][/tex]
2. Distribute the [tex]\(-2\)[/tex] on the right-hand side:
[tex]\[ y - 5 = -2x - 8 \][/tex]
3. To isolate [tex]\( y \)[/tex], add [tex]\( 5 \)[/tex] to both sides of the equation:
[tex]\[ y = -2x - 8 + 5 \][/tex]
4. Simplify the constant terms on the right-hand side:
[tex]\[ y = -2x - 3 \][/tex]
So, the equation in slope-intercept form is:
[tex]\[ y = -2x - 3 \][/tex]
Comparing this with the given options:
A. [tex]\( y = -2x - 8 \)[/tex] (not the same)
B. [tex]\( y = -2x - 3 \)[/tex] (same as what we derived)
C. [tex]\( y = -2x + 9 \)[/tex] (not the same)
D. [tex]\( y = -2x - 2 \)[/tex] (not the same)
Therefore, the correct answer is:
B. [tex]\( y = -2x - 3 \)[/tex]
1. Start with the original equation:
[tex]\[ y - 5 = -2(x + 4) \][/tex]
2. Distribute the [tex]\(-2\)[/tex] on the right-hand side:
[tex]\[ y - 5 = -2x - 8 \][/tex]
3. To isolate [tex]\( y \)[/tex], add [tex]\( 5 \)[/tex] to both sides of the equation:
[tex]\[ y = -2x - 8 + 5 \][/tex]
4. Simplify the constant terms on the right-hand side:
[tex]\[ y = -2x - 3 \][/tex]
So, the equation in slope-intercept form is:
[tex]\[ y = -2x - 3 \][/tex]
Comparing this with the given options:
A. [tex]\( y = -2x - 8 \)[/tex] (not the same)
B. [tex]\( y = -2x - 3 \)[/tex] (same as what we derived)
C. [tex]\( y = -2x + 9 \)[/tex] (not the same)
D. [tex]\( y = -2x - 2 \)[/tex] (not the same)
Therefore, the correct answer is:
B. [tex]\( y = -2x - 3 \)[/tex]
