To convert a point-slope form equation to slope-intercept form, we need to express the equation in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Given equation in point-slope form:
[tex]\[ y - 3 = \frac{1}{2}(x - 1) \][/tex]
We start by distributing the slope [tex]\(\frac{1}{2}\)[/tex] to the terms inside the parentheses:
[tex]\[ y - 3 = \frac{1}{2}x - \frac{1}{2} \][/tex]
Next, we solve for [tex]\( y \)[/tex] by isolating it on one side of the equation. To do this, add [tex]\( 3 \)[/tex] to both sides:
[tex]\[ y = \frac{1}{2}x - \frac{1}{2} + 3 \][/tex]
Combine the constant terms:
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]
Thus, the correct answer 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]
