Slope of a line parallel to the line through (4, −2) and (−3, 5) What is the slope of any line parallel to the line joining (4, −2) and (−3, 5)?

Introduction / Context:Parallel lines share the same slope. Compute the slope of the given line from two points, then use that value directly for any parallel line.

Given Data / Assumptions:

• Points: (x1, y1) = (4, −2), (x2, y2) = (−3, 5)
• Slope m = (y2 − y1) / (x2 − x1)

Concept / Approach:Compute m once; all parallels have identical m. Take care with signs in numerator and denominator for accuracy.

Step-by-Step Solution:

Verification / Alternative check:Reversing point order gives the same slope: (−2 − 5)/(4 − (−3)) = −7/7 = −1, confirming consistency.

Why Other Options Are Wrong:3/7 and −3/7 reflect partial differences; 1 is the negative inverse (perpendicular), not parallel.

Common Pitfalls:Sign mistakes in the denominator are common; always subtract coordinates in the same order for x and y.

Final Answer:−1