Algebra / Linear Functions
Modeling across tables, points, and equations
Tables, graphs, verbal descriptions, and equations can describe the same linear relationship. Convert between them by identifying slope and initial value.
Least you need to know
- Slope is change in output divided by change in input.
- The value at input 0 is the intercept.
- An intersection of two models is a shared input-output pair.
Key notation
- m — Slope or constant rate of change
- b — Initial value in $y=mx+b$
Worked example
From points $(1,6)$ and $(3,14)$, the slope is $(14-6)/(3-1)=4$. Using $y=4x+b$ and $(1,6)$ gives $b=2$, so $y=4x+2$.
Common mistakes
- Use the input interval when finding slope from a table.
- The first listed output is not always the intercept.
How to recognize it
- A table has equally spaced inputs.
- A graph or pair of points is described in words.
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