Final answer:
The slope of the line passing through points (5,1) and (2, -3) is 4/3, and the perpendicular slope to this line is -3/4. The provided answer choices do not correctly match these slopes.
Step-by-step explanation:
To find the slope of a line passing through two points (5,1) and (2, -3), we use the formula for slope, which is (change in y) / (change in x), or (y2-y1)/(x2-x1). In this case, the slope is (-3-1)/(2-5) = -4/-3, which simplifies to 4/3. Therefore, the slope of this line is 4/3.
Now, to find the perpendicular slope, we take the negative reciprocal of the original slope. This means we flip the fraction and change the sign. For a slope of 4/3, the negative reciprocal would be -3/4. So, the perpendicular slope to the line with slope 4/3 is -3/4.
None of the answer choices provided correctly identifies these slopes, suggesting that there may be a mistake in the question or the answer choices.