Linear Functions

Function notation describes input-output relationships. Linear function questions often ask for a function value, an input that gives a specified output, a rate of change, or a parameter in a function rule.

Linear function questions often ask for a rate of change, an initial value, a missing table value, or an equation that matches a real-world relationship.

A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.

A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.

A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.

A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.

Parameter questions for linear functions may ask for an unknown slope, intercept, or coefficient from function values or rate-of-change conditions.

Tables, graphs, verbal descriptions, and equations can describe the same linear relationship. Convert between them by identifying slope and initial value.

In a linear model, the constant term is the starting value and the coefficient of the input is the rate of change. The sign of the coefficient shows increase or decrease.

Contextual algebra problems often combine units, rates, initial values, and restrictions such as budgets or nonnegative amounts.