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# Linear function

| 🗖 nosplit | ↑ parent "Linear algebra" | words: 131
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The term is not very clear, as it could either mean:
• a real number function whose graph is a line, i.e.: $$f(x)=ax+b (83)$$ or for higher dimensions, a hyperplane: $$f(x1​,x2​,…,xn​)=c1​x1​+c2​x2​+…+cn​xn​+b (84)$$
• a linear map. Note that the above linear functions are not linear maps unless (known as the homogeneous case), because e.g.: $$f(x+y)=ax+ay+b (85)$$ but $$f(x)+f(y)=ax+b+ay+b (86)$$ For this reason, it is better never to refer to linear maps as linear functions.
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