Question 1145: Two-Point Slope of an Affine Graph

Original question and givens

Over the reals, an affine-function graph contains (7, 2) and (5, 9), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

• G001 — Over the reals, an affine-function graph contains (7, 2) and (5, 9), 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(5, 7)

Δx = -2

Δy := sub(9, 2)

Δy = 7

slope := div(7, -2)

slope = -7/2

slope·Δx := mul(-7/2, -2)

slope·Δx = 7

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

-7/2

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.