To convert the given point-slope form equation to slope-intercept form, follow these steps:
### Given Equation:
[tex]\[ y - 3 = \frac{1}{2}(x - 1) \][/tex]
### Step-by-Step Solution:
1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right side:
[tex]\[ y - 3 = \frac{1}{2}x - \frac{1}{2} \][/tex]
2. Isolate [tex]\(y\)[/tex] by adding 3 to both sides of the equation:
[tex]\[ y = \frac{1}{2}x - \frac{1}{2} + 3 \][/tex]
3. Combine the constants on the right side:
[tex]\[ y = \frac{1}{2}x + \left(3 - \frac{1}{2}\right) \][/tex]
[tex]\[ y = \frac{1}{2}x + \frac{6}{2} - \frac{1}{2} \][/tex]
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]
Thus, the slope-intercept form of the equation is:
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]
The correct answer is:
[tex]\[ \boxed{y = \frac{1}{2}x + \frac{5}{2}} \][/tex]
