Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A scientist is tracking the growth of a plant. The height of the plant in cm after 'd' days is given by the function H(d) = 0.5d + 10. What is the meaning of the number 10 in this function?
- AThe plant will reach 10 cm after 0.5 days.
- BThe initial height of the plant was 10 cm.
- CThe maximum height the plant will reach is 10 cm.
- DThe plant grows 10 cm per day.
Show answer & explanationAnswer & explanation
Correct answer: B. The initial height of the plant was 10 cm.
In a linear function H(d) = md + b, 'b' represents the y-intercept, which is the value of H(d) when d = 0. In this context, when d = 0 days, H(0) = 0.5(0) + 10 = 10, meaning the initial height of the plant was 10 cm.
Why the other options are wrong
- A. Substituting d = 0.5 into the function gives H(0.5) = 0.5(0.5) + 10 = 0.25 + 10 = 10.25 cm, not 10 cm.
- C. This function is linear and indicates continuous growth, not a maximum height.
- D. The growth rate (slope) is 0.5 cm per day, not 10.
Y-intercept in Linear Models
The constant term 'b' in a linear equation y = mx + b, representing the value of the dependent variable when the independent variable is zero.
- Often interpreted as the initial amount, starting value, or fixed cost.
- Graphically, it's the point where the line crosses the y-axis.
- It's the value of y when x = 0.
Memory trick: B is for Beginning, where the line crosses Y!