# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Affine and degree-one functions: finding m and b from two points, and deciding degree, zero and linearity](/en/derivations/derivation-mko-linear-function-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-linear-function)

The graph of the affine function f:ℝ→ℝ, f(x)=mx+b, passes through (1,4) and (3,0). Find m and b; decide whether f has degree one, find its zero, and decide whether f is an ℝ-linear map in the sense of linear algebra. Then prove that two affine functions are equal on ℝ exactly when their slopes and intercepts agree, and use it to explain why f(2)=k(2) (with k(x)=x) does not give f=k; finally treat the two degenerate examples with m=0, g(x)=5 and h(x)=0.

Affine functions and degree-one functions

derivation-mko-linear-function-01





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