Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsEasy
A botanist is studying the growth of a rare plant. The height of the plant 'H' (in cm) after 'd' days is given by the function H(d) = 2.5d + 15. What is the average rate of change of the plant's height between day 5 and day 15?
- A2.5 cm/day
- B15 cm/day
- C25 cm/day
- D5 cm/day
Show answer & explanationAnswer & explanation
Correct answer: A. 2.5 cm/day
For a linear function of the form y = mx + b, the rate of change is constant and equal to the slope 'm'. The given function H(d) = 2.5d + 15 is linear, so its rate of change is always 2.5 cm/day.
Why the other options are wrong
- B. This is the initial height (y-intercept) of the plant, not the rate of change.
- C. This could be a miscalculation of the total change over 10 days, or a sum.
- D. This might be a calculation error (e.g., (40-27.5)/5).
Average Rate of Change (Linear Function)
For a linear function, the average rate of change between any two points is constant and equal to the slope of the line.
- Formula: (y2 - y1) / (x2 - x1)
- For y = mx + b, rate of change is 'm'.
- Represents how much the dependent variable changes per unit change in the independent variable.
Memory trick: Linear Means Slope is Always the Rate.