Find the slope of the straight line passing through the points (8, 2) and (3, 1). Express the slope as a simplified fraction.

Introduction / Context: This question tests the slope formula for a line passing through two given points. Slope measures the rate of change of y with respect to x and is computed as “rise over run.” In coordinate geometry and aptitude, accurately substituting into the slope formula is essential, and simplifying the resulting fraction correctly is a common requirement.

Given Data / Assumptions:

• Point 1 = (8, 2) • Point 2 = (3, 1) • Required: slope m of the line through these points

Concept / Approach: Use the slope formula: m = (y2 - y1) / (x2 - x1). Any consistent order works as long as you subtract y and x in the same order. Then simplify the fraction. The sign of the slope indicates whether the line rises or falls as x increases.

Step-by-Step Solution: 1) Identify (x1, y1) = (8, 2) and (x2, y2) = (3, 1) 2) Apply the slope formula: m = (y2 - y1) / (x2 - x1) 3) Substitute values: m = (1 - 2) / (3 - 8) 4) Compute differences: 1 - 2 = -1 3 - 8 = -5 5) Divide: m = (-1)/(-5) = 1/5

Verification / Alternative check: A quick interpretation check: moving from x = 3 to x = 8 increases x by 5 while y increases from 1 to 2, which is an increase of 1. So rise/run = 1/5, matching the computed slope. The slope is positive, which makes sense because y increases as x increases across these two points.

Why Other Options Are Wrong: • 5 is the reciprocal (run/rise) and not the slope. • 3/5 and 5/3 come from incorrect subtraction or mixing points. • -1/5 would happen if only one difference is made negative (inconsistent subtraction).

Common Pitfalls: • Subtracting y values in one order and x values in the opposite order. • Forgetting that negative divided by negative becomes positive.

Final Answer: 1/5