Final answer:
The equation of a line perpendicular to y = x/2 + 3 and passing through (1,8) is y = -2x + 10. A review of the provided answer choices reveals none match this equation, indicating a potential mistake in the choices.
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to a given line and passes through a specific point. The given line's equation is y = x/2 + 3, which has a slope of 1/2. A line perpendicular to this one will have a slope that is the negative reciprocal of 1/2, which is -2.
Now, using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the point (1, 8) and m is the slope -2, we get:
y - 8 = -2(x - 1).
Simplifying this equation we get:
y = -2x + 10.
This equation must be compared with the options to find the correct one. Upon examining the options, it appears that none of them match the simplified equation, indicating a possible mistake in the choices provided. However, if we consider option B, y = -2x + 7, it is clear there is an error. To ensure accuracy and relevance, this discrepancy should be acknowledged.