Algebra / Linear Functions
Linear Function Tables, Rates, and Models
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.
Least you need to know
- The rate of change is the change in output divided by the change in input.
- For $f(x)=mx+b$, $m$ is the rate of change and $b=f(0)$.
- A linear table has a constant rate of change.
Key notation
- $f(x)=mx+b$ — A linear function with rate of change $m$ and initial value $b$
Worked example
- If $f(2)=9$ and $f(6)=21$, the rate of change is $\frac{21-9}{6-2}=3$.
- The output increases by 3 for each increase of 1 in the input.
Common mistakes
- Use change in output over change in input, not the reverse.
- Do not assume the first table entry is the initial value unless $x=0$.
How to recognize it
- The problem gives a table of values.
- The problem asks for rate of change or initial value.
- The problem asks for the equation of a linear function.
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