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## Sagot :

Here are the steps:

1. Start with the point-slope form equation:

[tex]\[ y - 8 = \frac{1}{2}(x - 4) \][/tex]

2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right-hand side:

[tex]\[ y - 8 = \frac{1}{2} x - \frac{1}{2} \cdot 4 \][/tex]

[tex]\[ y - 8 = \frac{1}{2} x - 2 \][/tex]

3. Isolate [tex]\(y\)[/tex] by adding 8 to both sides of the equation:

[tex]\[ y - 8 + 8 = \frac{1}{2} x - 2 + 8 \][/tex]

[tex]\[ y = \frac{1}{2} x + 6 \][/tex]

Thus, the linear function that represents the line is:

[tex]\[ r(x) = \frac{1}{2} x + 6 \][/tex]

Therefore, the correct option is:

[tex]\[ r(x) = \frac{1}{2} x + 6 \][/tex]