Final answer:
Using the point-slope form, the correct equation of the line passing through (2, -1) with a slope of 3 is y = 3x - 7. None of the provided options match this equation, and thus, none of them correctly represents the line described.
Step-by-step explanation:
To determine which equation represents a line that passes through the point (2, -1) with a slope of 3, we can use the point-slope form of a linear 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 of the line.
Using the given point (2, -1) and the slope 3, the equation of the line is y - (-1) = 3(x - 2). Simplifying this, we get y + 1 = 3x - 6, and then y = 3x - 6 - 1, which results in y = 3x - 7. None of the given options match this equation exactly, but since there might be a typo, we look for the closest match that has the correct slope and passes through the given point.
Reviewing the options, we see that option A) y - 2 = 3(x + 3) simplifies to y = 3x + 9 - 2, which is y = 3x + 7. This equation does not pass through the point (2, -1), so it's not correct. Option B) y - 3 = 2(x + 3) has a slope of 2, which is not the correct slope. Options C and D are not even in the correct format of a linear equation in two variables (they contain a variable z that is not part of the original question).
Therefore, with the information provided and despite the typos in the options, we can conclude that none of the given options correctly represents the line described in the question.