Sure, let's convert the given equation [tex]\( y - 2 = 3(x + 1) \)[/tex] from point-slope form to slope-intercept form step-by-step.
1. Start with the given equation:
[tex]\[
y - 2 = 3(x + 1)
\][/tex]
2. Distribute the 3 on the right-hand side of the equation:
[tex]\[
y - 2 = 3x + 3
\][/tex]
3. Add 2 to both sides of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[
y - 2 + 2 = 3x + 3 + 2
\][/tex]
4. Simplify the equation:
[tex]\[
y = 3x + 5
\][/tex]
So, the slope-intercept form of the equation [tex]\( y - 2 = 3(x + 1) \)[/tex] is:
[tex]\[
y = 3x + 5
\][/tex]
Therefore, the correct choice is:
[tex]\[
y = 3x + 5
\][/tex]
