Linear Functions Practice Flashcards

A set of vocabulary flashcards covering the core concepts of linear functions, gradients, and algebraic modelling.

Linear number pattern

A list of numbers that increases or decreases by the same amount for each new term.

Linear

An adjective meaning "of a line".

Function

An algebraic rule that behaves like a "number machine," taking input $x$ and producing output $y$.

Gradient ($m$)

A number that gives a measure of the steepness of a line, calculated by $\text{gradient} = \frac{\text{rise} \text{ } \text{(vertical change)}}{\text{run} \text{ } \text{(horizontal change)}}$.

$y$-intercept ($b$)

The value where a line crosses the $y$-axis.

Formula for a straight line

$$y = mx + b$$

Positive gradient

A slope that goes upwards because $y$ increases as $x$ increases, such as in the function $y = 3x - 2$.

Negative gradient

A slope that goes downwards because $y$ decreases as $x$ increases, such as in the function $y = -4x + 1$.

Gradient formula

$$m = \frac{\text{change in } y}{\text{change in } x}$$

Algebraic modelling

The process where researchers and scientists observe patterns in nature and use mathematical formulae to represent a real-life situation.

Linear model

A linear function $y = mx + b$ that models a real-life situation.

Independent variable

The $x$ variable in a linear model.

Dependent variable

The $y$ variable in a linear model.

Vertical intercept

In a linear model, the starting value of $y$ represented by the variable $b$.