Question

1. the height of a plant was measured regularly over the course of a year. the height, in centimeters, of the plant shows a strong linear relationship with the number of weeks, x, since it was planted. the relationship can be modeled by the function f(x) = 5x + 15. what is the meaning of the y-intercept of this function?

• the height of the plant increases by about 5 centimeters per week.
• the height of the plant increases by about 15 centimeters per week.
• the plant was about 5 centimeters tall when planted.
• the plant was about 15 centimeters tall when planted.

Explanation:

The function \(f(x) = 5x + 15\) follows the linear form \(y = mx + b\), where \(b\) is the y-intercept. The y-intercept occurs at \(x = 0\) (when the plant was planted, 0 weeks since planting). Substituting \(x = 0\) gives \(f(0) = 15\), meaning the plant's initial height was 15 cm.

Answer:

D. The plant was about 15 centimeters tall when planted.