Final answer:
The equation of the line passing through the point (2, -3) and perpendicular to the line y = 3x - 5 is found by taking the negative reciprocal of the slope, which is -1/3, and using the point-slope formula. The correct equation is y = -1/3x - 7/3, which does not match any of the provided options.
Step-by-step explanation:
The student has asked to write an equation of the line passing through the point (2, -3) and perpendicular to the line y = 3x - 5. To find a line perpendicular to another, we need to find the negative reciprocal of the original line's slope. Since the slope of the given line is 3, the slope of the perpendicular line will be -1/3. Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting in our point (2, -3) and our slope -1/3, we get y - (-3) = -1/3(x - 2), which simplifies to y + 3 = -1/3x + 2/3. To get this in the form y = mx + b, we subtract 3 from both sides, resulting in y = -1/3x + 2/3 - 3, or y = -1/3x - 7/3. Now, we look at the options provided and see if any match our equation. To match the form y = mx + b, we need to convert -7/3 into a number with a whole number denominator if possible. Since -7/3 cannot be simplified further and doesn't match any of the given options, we need to check our work for possible multiplication or arithmetic errors. After reviewing the work, we notice 2/3 - 3 simplifies to 2/3 - 9/3, which is -7/3, not -1 or +1. No calculation errors are found, so it seems there might be a mistake in the options provided, as none of them correctly matches the equation we have found.