Answer:
C
Step-by-step explanation:
To convert from point-slope form to slope-intercept form, we can simplify and isolate the y.
We have the equation:
[tex]\displaystyle y-3=\frac{1}{2}(x-1)[/tex]
Distribute the right-hand side:
[tex]\displaystyle y-3=\frac{1}{2}x-\frac{1}{2}[/tex]
Add 3 to both sides:
[tex]\begin{aligned} \displaystyle y&=\frac{1}{2}x-\frac{1}{2}+3\\\\&=\frac{1}{2}x-\frac{1}{2}+\frac{6}{2}\\\\&=\frac{1}{2}x+\frac{5}{2}\end{aligned}[/tex]
Our answer is C.
