Final answer:
The equation of the line perpendicular to y = -1/2x + 6 and passing through (-6, 1) is y = 2x + 13, which is option B.
Step-by-step explanation:
The student's question is asking to write an equation of a line that is perpendicular to the given line y = -1/2x + 6 and passes through the point (-6, 1). To solve this, we should first understand that the slope of the line we are looking for will be the negative reciprocal of the slope of the given line. Since the slope of the given line is -1/2, the slope of the perpendicular line will be 2 (negative reciprocal of -1/2).
Next, we use the point-slope form of the equation of a line which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Thus, plugging in the point (-6, 1) and the slope m = 2, we get:
y - 1 = 2(x + 6)
Expanding this equation, we get:
y - 1 = 2x + 12
Adding 1 to both sides of the equation to solve for y, we obtain:
y = 2x + 13
Therefore, the correct equation of the line is B) y = 2x + 13.