Question

1 * A botanist collected data on the growth of sunflowers to maturity. She modeled the equation y = x + for the line of best fit. The independent variable, 2 x, is time in weeks and the dependent variable, y, is height in feet. What does the y-intercept mean in this context? A The sunflower's starting height is 1 foot. B 1 The sunflower's starting height is foot. 2 C The sunflower's height increases by an additional 1 foot each week. D 1 The sunflower's height increases by an additional foot each week. 2

Answer 1

To determine the meaning of the y-intercept in the context of the given equation \( y = x + 1 \), we first need to clarify the components of the equation:

• \( y \) is the height of the sunflower in feet (dependent variable).
• \( x \) is the time in weeks (independent variable).
• The y-intercept is the value of \( y \) when \( x = 0 \).

In this equation, the y-intercept occurs when \( x = 0 \): \[ y = 0 + 1 = 1 \] Thus, the y-intercept is 1.

In the context of the sunflower's growth:

• When \( x = 0 \) (at the start, before any time has passed), the height of the sunflower (y) is 1 foot.

Given this analysis, the correct interpretation of the y-intercept is: A The sunflower's starting height is 1 foot.