To convert the given equation from point-slope form to slope-intercept form, we need to simplify the equation step by step.
Given equation:
[tex]\[ y - 2 = 3(x + 1) \][/tex]
1. Distribute the 3 on the right side:
[tex]\[ y - 2 = 3 \cdot x + 3 \][/tex]
2. Simplify the equation:
[tex]\[ y - 2 = 3x + 3 \][/tex]
3. Add 2 to both sides to solve for \( y \):
[tex]\[ y = 3x + 3 + 2 \][/tex]
4. Combine like terms:
[tex]\[ y = 3x + 5 \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = 3x + 5 \][/tex]
Therefore, the correct option is:
[tex]\[ y = 3x + 5 \][/tex]
