Find the slope of a straight line that is parallel to the line passing through the points (4, -2) and (-3, 5).

Introduction / Context:
This question checks your understanding of the concept of slope in coordinate geometry and the fact that parallel lines have equal slopes. Given two points, you must compute the slope of the line joining them, and then use that slope for any line parallel to it. This is a very common pattern in algebra and analytic geometry questions.

Given Data / Assumptions:

• Two points on the given line: (4, -2) and (-3, 5).
• We must find the slope of a line parallel to this given line.
• In the coordinate plane, slope m = (change in y) / (change in x).

Concept / Approach:
The slope m of a line passing through points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1).
Parallel lines have equal slopes. So once we compute the slope of the line through the given points, that same value is the slope of any line parallel to it. The rest is straightforward substitution and simplification.

Step-by-Step Solution:
Step 1: Label the points as (x1, y1) = (4, -2) and (x2, y2) = (-3, 5). Step 2: Use the slope formula m = (y2 - y1) / (x2 - x1). Compute y2 - y1 = 5 - (-2) = 5 + 2 = 7. Compute x2 - x1 = -3 - 4 = -7. Step 3: Therefore m = 7 / (-7) = -1. Step 4: Any line parallel to this line must have the same slope m = -1.

Verification / Alternative check:
We can check by interchanging the roles of the points. If we take (x1, y1) = (-3, 5) and (x2, y2) = (4, -2), then m = (y2 - y1) / (x2 - x1) = (-2 - 5) / (4 - (-3)) = (-7) / 7 = -1 again. The slope is unchanged, confirming that our computation is consistent. Since parallel lines share the same slope, the required slope must be -1.

Why Other Options Are Wrong:
Option A (3/7): This could arise from incorrect subtraction or partial simplification but does not match the correct ratio of changes. Option B (1): This would correspond to a line rising one unit for every one unit of x, which is not the case here. Option C (-3/7): This suggests mixing up the differences in x and y. Option E (0): This would imply a horizontal line, which is not supported by the coordinates given.

Common Pitfalls:
A frequent mistake is to reverse the order of subtraction inconsistently between numerator and denominator, which changes the sign of the slope. Another issue is misreading the coordinates, especially the negative signs. As long as you subtract in the same order for x and y coordinates, the sign will be correct. Also remember that parallel lines share the same slope, so once the slope is correctly computed, that is the final answer.

Final Answer:
The slope of any line parallel to the given line is -1.