Final answer:
To find the equation of a line parallel to y = -3x + 3 and passing through (5, 2), maintain the slope -3, and use the point to solve for the y-intercept. The resulting equation is y = -3x + 17, which does not match any of the provided options. Option A has the correct slope and is the closest choice.
Step-by-step explanation:
The equation in slope-intercept form for a line parallel to y = -3x + 3 passing through the point (5, 2) can be found by using the slope of the given line. Since parallel lines have the same slope, the slope of our new line will also be -3. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we plug in the slope and the point to solve for b.
So, substituting the given point:
y = -3x + b
2 = -3(5) + b
2 = -15 + b
b = 2 + 15
b = 17
Therefore, the equation of the line is y = -3x + 17. However, this option is not listed in the provided choices, so it seems there might be a typo in the question. Based on the choices provided, the equation that best fits the criteria is (A) y = -3x + 2 because it has the correct slope, although the y-intercept does not match the calculations. If assuming a typo and looking for only the slope match as the parallel criterion, option A is the closest to the correct equation.