Final answer:
The equation of the line parallel to y = -1/2x - 1 and passing through the point (6, 2) is y = -1/2x + 5.
Step-by-step explanation:
To write the equation of a line that is parallel to a given line and that passes through a specific point, you must first understand that parallel lines have the same slope. The line provided y = -1/2x - 1 has a slope of -1/2. Therefore, the line we want to find will also have this slope. Since the line must pass through the point (6, 2), we use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Substituting our point and slope into the point-slope formula, we get:
y - 2 = -1/2(x - 6)
Now, we simplify and put the equation into slope-intercept form y = mx + b to get our final answer:
y - 2 = -1/2x + 3
y = -1/2x + 5
Therefore, the equation of the line is y = -1/2x + 5.