Final answer:
Since line B is parallel to line A with a slope of 1/3 and passes through the point (-3, 1), the correct equation of line B should be y = (1/3)x + 2. However, a typo in the provided options suggests Option 2 is the closest correct answer, even though it appears the options contain an error.
Step-by-step explanation:
The question is asking to identify the equation of line B that is parallel to line A with the given equation y = (1/3)x + 4 and passes through the point (-3, 1). Because line B is parallel to line A, they must have the same slope. The slope of line A is 1/3, hence line B also has a slope of 1/3. To find the equation of line B in slope-intercept form, which is y = mx + b, we use the slope m = 1/3 and the point (-3, 1) to solve for b, the y-intercept.
We plug the point into the slope-intercept equation:
1 = (1/3)(-3) + b
1 = -1 + b
b = 2
So the equation of line B is y = (1/3)x + 2, which matches Option 1: y = (1/3)x - 2. However, since we found b to be 2 and Option 1 indicates -2, there is a typo in the provided options. The correct equation would be y = (1/3)x + 2 if available in the options. If not, based on the given options, Option 2: y = (1/3)x + 1, is the closest match that fits the criteria of the question still acknowledging that there appears to be an error in the provided options.