To convert the given point-slope form equation [tex]\( y - 2 = 3(x + 1) \)[/tex] into slope-intercept form (which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept), follow these steps:
1. Distribute the 3 on the right-hand side:
[tex]\[
y - 2 = 3x + 3
\][/tex]
2. Isolate [tex]\( y \)[/tex] by adding 2 to both sides of the equation:
[tex]\[
y - 2 + 2 = 3x + 3 + 2
\][/tex]
Simplifying the left side, we get:
[tex]\[
y = 3x + 5
\][/tex]
Now, the equation is in slope-intercept form. Therefore, the slope-intercept form of the equation is:
[tex]\[
y = 3x + 5
\][/tex]
The correct answer is:
[tex]\[
y = 3x + 5
\][/tex]
