Final answer:
The equation of a line parallel to y = 3x - 1 that passes through the point (-2, 3) is y = 3x + 9. The equation of a line parallel to y = 3x - 1 that passes through the point (-2, 3) is y = 3x + 9 (option b).
Step-by-step explanation:
The equation of a line parallel to y = 3x - 1 will also have a slope of 3 because parallel lines have the same slope. We can use the point-slope form of a line to find the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Given that the line passes through the point (-2, 3) and has a slope of 3, we can substitute these values into the point-slope form:
y - 3 = 3(x - (-2))
Simplifying the equation, we get y - 3 = 3x + 6.
Therefore, the equation of a line parallel to y = 3x - 1 that passes through the point (-2, 3) is y = 3x + 9 (option b).