Final answer:
The correct equation of the line parallel to x + 2y = 6 and passing through (8, 3) is Option 1: x + 2y = 14, as it maintains the same slope of -1/2.
Step-by-step explanation:
The student asks for the equation of a line that passes through the point (8, 3) and is parallel to the line described by x + 2y = 6. To maintain parallelism, the new equation must have the same slope. Because the original line can be rewritten as y = -1/2 x + 3, it has a slope of -1/2. The new line must have this same slope, and it must pass through (8, 3). The options should therefore reflect this slope. Inserting the point into the original equation's form, we get 8 + 2(3) = 14, which suggests the correct equation is x + 2y = 14. This ensures that the coefficients of x and y are the same in both the original and new equations, indicating parallel lines. Therefore, Option 1: x + 2y = 14 is the correct answer.