To determine the slope-intercept form of the given equation [tex]\( y + 3 = 4(x - 5) \)[/tex], let's follow these steps:
1. Start with the given equation:
[tex]\[ y + 3 = 4(x - 5) \][/tex]
2. Distribute the 4 on the right-hand side:
[tex]\[ y + 3 = 4x - 20 \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 3 from both sides:
[tex]\[ y = 4x - 20 - 3 \][/tex]
[tex]\[ y = 4x - 23 \][/tex]
Now, we have the equation in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Comparing with the given options:
- Option 1: [tex]\( y = 4x - 8 \)[/tex]
- Option 2: [tex]\( y = 4x + 2 \)[/tex]
- Option 3: [tex]\( y = 4x + 17 \)[/tex]
- Option 4: [tex]\( y = 4x - 23 \)[/tex]
The correct form is:
[tex]\[ y = 4x - 23 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
