Final answer:
The equation of the line that passes through (-1, 2) and is parallel to the line with x-intercept (3, 0) and y-intercept (0, 1) is y = (-1/3)x + 5/3. This is not listed in the options (a-d), but would be the one with the slope of -1/3 if it were present.
Step-by-step explanation:
To find the equation of the line that is parallel to another line with given intercepts, we first need to determine the slope of that reference line. The given reference line has intercepts at (3, 0) and (0, 1). This means the slope (m) is found by the difference in the y-coordinates divided by the difference in the x-coordinates, which is (1 - 0) / (0 - 3) or -1/3. Since parallel lines have equal slopes, the slope of our line is also -1/3.
Now, using the slope-intercept form of a line, y = mx + b, and the point (-1, 2) that the line must pass through, we substitute the slope and the point to find the y-intercept (b):
2 = (-1/3)(-1) + b
2 = 1/3 + b
b = 2 - 1/3
b = 5/3
Therefore, the equation of our line is y = (-1/3)x + 5/3, which is not explicitly listed in the options (a-d). However, if the options were to contain the correct equation, it would be the one with the slope of -1/3.