B: y = 1/2x - 3/2
Step-by-step explanation:
Given points M (-3, 2) and N (1, 4):
The slope of line MN can be determined using the slope formula:
![m = \frac{y2 - y1}{x2 - x1} = \frac{4 - 2}{1 - (- 3)} = \frac{2}{4} = \frac{1}{2}](/tpl/images/2478/7424/6a7d5.png)
Therefore, the slope of line MN = 1/2.
By definition, parallel lines have equal slopes. Since the slope of line MN = 1/2, then it means that the slope of the other line parallel to line MN must also be 1/2.
Therefore, the correct answer is B: y = 1/2x - 3/2.