Is y = 5 a linear function?

Yes, it is a constant linear function (where the slope m=0). Its graph is a horizontal line.

What is the difference between a linear function and a linear equation?

A linear function is a specific type of relationship between variables (often expressed as f(x) = mx + c). A linear equation is any equation that equates two linear expressions (e.g., 2x + 3 = 7). Every linear function can be written as a linear equation (y = mx + c), but not all linear equations define y as a function of x (e.g., x = 5).

Can a linear function be curved?

No, by definition, the graph of a linear function (in its elementary sense) is always a straight line. If the graph is curved, it represents a nonlinear function.

Why is it called 'linear'?

It comes from the Latin 'linea', meaning 'line'. The term directly references the straight-line graph of the function in Cartesian coordinates.

Is “linear function” formal?

Linear function is usually academic, technical in register.

How do you pronounce “linear function”?

Linear function: in British English it is pronounced /ˈlɪn.i.ə ˈfʌŋk.ʃən/, and in American English it is pronounced /ˈlɪn.i.ɚ ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.

linear function: meaning, definition, pronunciation and examples

UK/ˈlɪn.i.ə ˈfʌŋk.ʃən/US/ˈlɪn.i.ɚ ˈfʌŋk.ʃən/

Academic, Technical

My Flashcards

Quick answer

What does “linear function” mean?

A mathematical function whose graph is a straight line, typically of the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept.

Audio

Pronunciation

Definition

Meaning and Definition

A mathematical function whose graph is a straight line, typically of the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept.

More broadly, in advanced mathematics, it can refer to any function between vector spaces that preserves vector addition and scalar multiplication (additivity and homogeneity). In general usage, it describes any relationship or process that progresses in a direct, proportional manner without deviation.

Dialectal Variation

British vs American Usage

Differences

No significant differences in definition. British English is more likely to use the term 'gradient' for 'slope', and the constant term is often called 'c' or 'k' instead of 'b'.

Connotations

Identical. Strictly mathematical.

Frequency

Similar frequency in academic and STEM contexts. Slightly more common in American textbooks at secondary school level due to curriculum differences.

Grammar

How to Use “linear function” in a Sentence

NOUN + of + linear functionADJECTIVE + linear functionlinear function + VERB-ing (e.g., linear function representing)linear function + PREPOSITION + variable (e.g., linear function in x)

Vocabulary

Collocations

strong

plot a linear functiongraph of a linear functionequation of a linear functionslope of a linear functiondefine a linear function

medium

simple linear functioncontinuous linear functionreal-valued linear functionlinear function in two variablesmodel using a linear function

weak

basic linear functionstandard linear functionunderlying linear functionparticular linear function

Examples

Examples of “linear function” in a Sentence

adjective

British English

The model requires a linear function relationship.
We need a linear-function approximation.

American English

The model requires a linear function relationship.
We need a linear-function approximation.

Usage

Meaning in Context

Business

Rare. May appear in data analysis or forecasting: 'We initially assumed a linear function for cost growth.'

Academic

Core term in mathematics, physics, economics, and engineering courses. 'The relationship between force and extension is described by a linear function within the elastic limit.'

Everyday

Very rare, except in metaphorical sense: 'Life isn't a linear function; it has ups and downs.'

Technical

Fundamental concept in algebra, machine learning (linear models), and scientific modelling.

Vocabulary

Synonyms of “linear function”

Strong

affine function (if c ≠ 0, technically distinct in pure maths)linear map (in advanced contexts)

Neutral

first-degree polynomialstraight-line functionlinear equation (when solved for y)

Weak

proportional relationship (for direct variation, a specific case)constant rate of change

Vocabulary

Antonyms of “linear function”

nonlinear functionquadratic functionexponential function logarithmic functionpolynomial function of degree >1

Watch out

Common Mistakes When Using “linear function”

Confusing 'linear function' with 'linear equation' (the function is the relationship, the equation is one way to express it).
Assuming all straight-line graphs represent linear functions (vertical lines are not functions).
Using 'linear' to mean 'sequential' in a strict mathematical context where it is incorrect.

FAQ

Frequently Asked Questions

: Yes, it is a constant linear function (where the slope m=0). Its graph is a horizontal line.
: A linear function is a specific type of relationship between variables (often expressed as f(x) = mx + c). A linear equation is any equation that equates two linear expressions (e.g., 2x + 3 = 7). Every linear function can be written as a linear equation (y = mx + c), but not all linear equations define y as a function of x (e.g., x = 5).
: No, by definition, the graph of a linear function (in its elementary sense) is always a straight line. If the graph is curved, it represents a nonlinear function.
: It comes from the Latin 'linea', meaning 'line'. The term directly references the straight-line graph of the function in Cartesian coordinates.
: A mathematical function whose graph is a straight line, typically of the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept.
: Linear function is usually academic, technical in register.
: Linear function: in British English it is pronounced /ˈlɪn.i.ə ˈfʌŋk.ʃən/, and in American English it is pronounced /ˈlɪn.i.ɚ ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.

Phrases

Idioms & Phrases

“To think in linear terms”
“A linear progression (metaphorical use)”

Learning

Memory Aids

Mnemonic

LINear Function: Like a LINE, it's straight. Think of the 'line' in 'linear'.

Conceptual Metaphor

STRAIGHTNESS IS PREDICTABILITY / SIMPLICITY (e.g., a linear argument, linear thinking).

Practice

Quiz

Fill in the gap

The relationship between Celsius and Fahrenheit is a , expressible by the formula F = 1.8C + 32.

Multiple Choice

Which of the following best describes the graph of a linear function in two variables?