SAT Math: Interpreting Slope in Context
37+ practice questions in Praczo
The concept, explained
- 1
Slope (m in y = mx + b) is the rate of change: the change in y for every 1-unit change in x.
- 2
In word problems, slope represents "amount per unit" (e.g., dollars per hour, miles per gallon, people per year).
- 3
A positive slope indicates an increase or growth; a negative slope indicates a decrease or decay.
- 4
Read the units of both axes or variables carefully. Slope units are always (units of y) / (units of x).
- 5
Watch for questions asking for the change over MULTIPLE units (e.g., "how much does it increase over 3 years?" → 3m).
- ✗ Reversing the variables in the description (saying x changes for every 1 unit of y, rather than y changing for every 1 unit of x).
- ✗ Ignoring a negative sign and describing a decrease as an increase.
SAT-style practice
A company's profit P, in thousands of dollars, is modeled by P = 15x − 20, where x is the number of years since 2015. What does the number 15 represent?
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