Final answer:
The equation of the line passing through the given point (3, 6) with a slope of -2 is found using the point-slope formula and simplifying, leading to the answer y = -2x + 12.
Step-by-step explanation:
The question asks to find the equation of the line that passes through the point (3, 6) with a given slope of -2. To find this equation, we can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the given point and slope, we get y - 6 = -2(x - 3).
Simplifying this, we get y = -2x + 12. Therefore, the correct answer is option a: y = -2x + 12.