Question

which linear function represents the line given by the point-slope equation $y - 8 = \frac{1}{2}(x - 4)$?○ $f(x) = \frac{1}{2}x + 4$○ $f(x) = \frac{1}{2}x + 6$○ $f(x) = \frac{1}{2}x - 10$○ $f(x) = \frac{1}{2}x - 12$

Explanation:

Step1: Expand the right-hand side

$y - 8 = \frac{1}{2}x - \frac{1}{2} \times 4$
$y - 8 = \frac{1}{2}x - 2$

Step2: Isolate y by adding 8

$y = \frac{1}{2}x - 2 + 8$
$y = \frac{1}{2}x + 6$

Step3: Rewrite as function $f(x)$

$f(x) = \frac{1}{2}x + 6$

Answer:

$\boldsymbol{f(x) = \frac{1}{2}x + 6}$ (Option C)