SAT Math: Interpreting Slope as Rate of Change
36+ practice questions in Praczo
The concept, explained
- 1
In a real-world linear model, the slope represents how much the output changes for each one-unit increase in the input. It has units: (y-units) per (x-unit).
- 2
A positive slope means the quantity is increasing; a negative slope means it is decreasing. A slope of 0 means no change.
- 3
The SAT often gives an equation like C = 15h + 50 and asks what 15 represents. Answer: the cost increases by $15 for each additional hour.
- 4
Do not confuse slope (rate of change) with the y-intercept (starting value). In C = 15h + 50, the $50 is the initial amount and $15/hr is the rate.
- 5
Units of slope are always (units of y) per (unit of x). If y is in dollars and x is in hours, slope is dollars per hour.
- ✗ Interpreting the y-intercept as the rate of change — the intercept is the initial or fixed value, not how fast something is changing.
- ✗ Getting units backwards: if slope = 15 and x is in hours, the rate is 15 (y-units) per hour, not 15 hours per (y-unit).
SAT-style practice
A plumber charges according to the equation C = 65h + 120, where C is the total cost in dollars and h is the number of hours worked. What does 65 represent in this context?
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