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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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اس موضوع کو Linear Functions کے ساتھ جاری رکھیں۔

Linear Functions

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Linear Function Notation and Inputs Linear Functions Linear Functions

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