Algebra / Linear Functions
Rates and intercepts in models
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.
Least you need to know
- Positive rates increase the output.
- Negative rates decrease the output.
- The intercept is the output when the input is 0.
Key notation
- r — A constant rate of change
Worked example
For $A=80-5t$, the starting amount is 80 and the amount decreases by 5 for each 1-unit increase in $t$.
Common mistakes
- A decrease should be represented with a negative rate.
- The intercept and rate have different units.
How to recognize it
- The problem asks what a number in an equation represents.
- A context gives an initial amount and a per-unit change.
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