A botanist collected data on the growth of sunflowers to maturity.
She modeled the equation y=x+32
for the line of best fit.
The independent variable, x, is time in weeks and the dependent variable, y, is height in feet. What does the slope mean in this context?
(1 point)
Responses
The sunflower's height increases by an additional 1 foot each week.
The sunflower's height increases by an additional 1 foot each week.
The sunflower's starting height is 3/2 foot.
The sunflower's starting height is 3/2 foot.
The sunflower's height increases by an additional 3/2 foot each week.
The sunflower's height increases by an additional 3/2 foot each week.
The sunflower's age increases by an additional 3/2 week every 1 foot.
The sunflower's age increases by an additional 3/2 week every 1 foot.
The sunflower's starting height is 1 foot.
The sunflower's starting height is 1 foot.
The equation of the line of best fit provided is y = x + 32, where y is the height in feet and x is time in weeks. In the context of this equation, the slope is represented by the coefficient of the independent variable x, which in this case is 1 (since there's no coefficient written, it's understood to be 1).
The slope of a line in a linear equation such as y = mx + b indicates how much the dependent variable (y) changes for every one unit increase in the independent variable (x). In this scenario, since the slope (m) is 1, it means that for every additional week, the height of the sunflower increases by 1 foot.
Therefore, the response that accurately describes the meaning of the slope in this context is:
The sunflower's height increases by an additional 1 foot each week.