Final answer:
The equation of a line parallel to y = -2x + 3 that passes through (6, 1) is y = -2x + 13. The provided options do not include the correct equation, suggesting a possible error in the question choices.
Step-by-step explanation:
The equation of the line parallel to the line represented by y = -2x + 3 and passing through the point (6, 1) can be found using the concept that parallel lines have equal slopes. The slope of the given line is -2, hence the slope of the line we seek (m) is also -2. The slope-intercept form of a line equation is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope m = -2 and the point (6, 1), we can find b by plugging the values into the equation:
y = (-2)x + b
1 = (-2)(6) + b
1 = -12 + b
b = 1 + 12
b = 13
Therefore, the equation of the line in slope-intercept form is y = -2x + 13, which is not present in the provided options. The closest option to the correct answer is b) y = -2x - 9, but it still differs in the y-intercept value. It seems there may be an error in the provided options.