Question 1141: Two-Point Slope of an Affine Graph

Original question and givens

Over the reals, an affine-function graph contains (3, -2) and (-1, 1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

• G001 — Over the reals, an affine-function graph contains (3, -2) and (-1, 1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-linear-function

Step-by-step derivation

f:R→R; f(x)=mx+b

m=0 gives a constant affine function

Δx := sub(-1, 3)

Δx = -4

Δy := sub(1, -2)

Δy = 3

slope := div(3, -4)

slope = -3/4

slope·Δx := mul(-3/4, -4)

slope·Δx = 3

Reverse checks

• S005 · premise_and_result_audit — Recompute slope·Δx with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute slope with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute Δy with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute Δx with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

-3/4

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.