To convert the given point-slope equation [tex]\( y + 3 = 4(x - 5) \)[/tex] into slope-intercept form, we follow these steps:
1. Distribute the 4 on the right side:
[tex]\[
y + 3 = 4(x - 5)
\][/tex]
[tex]\[
y + 3 = 4 \cdot x - 4 \cdot 5
\][/tex]
[tex]\[
y + 3 = 4x - 20
\][/tex]
2. Isolate [tex]\( y \)[/tex] by subtracting 3 from both sides:
[tex]\[
y + 3 - 3 = 4x - 20 - 3
\][/tex]
[tex]\[
y = 4x - 23
\][/tex]
Therefore, the slope-intercept form of the given equation is:
[tex]\[
y = 4x - 23
\][/tex]
Looking at the provided choices, the correct answer is:
[tex]\[
y = 4x - 23
\][/tex]
