Question
Week 7 - Math 8 - Assessment
5 of 115 of 11 Items
Question
A botanist collected data on the growth of sunflowers to maturity. She modeled the equation y = x + 1/2
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?
Responses
The sunflower's starting height is 1 foot.
The sunflower's starting height is 1 foot.
The sunflower's height increases by an additional
foot each week
The sunflower's height increases by an additional 1 halffoot each week
The sunflower's starting height is
foot
The sunflower's starting height is 1 halffoot
The sunflower's height increases by an additional 1 foot each week.
Answers
GPT-4o mini
In the equation \( y = x + \frac{1}{2} \), the coefficient of \( x \) is 1, which represents the slope of the line.
In this context:
- The slope of 1 means that for each week (1 unit increase in \( x \)), the height of the sunflower (the dependent variable \( y \)) increases by 1 foot.
The \( \frac{1}{2} \) part of the equation signifies the y-intercept, which indicates that when time (weeks) is zero (at the start), the sunflower's height is \( \frac{1}{2} \) foot.
So, the correct interpretation of the slope in this context is:
**The sunflower's height increases by an additional 1 foot each week.**
In this context:
- The slope of 1 means that for each week (1 unit increase in \( x \)), the height of the sunflower (the dependent variable \( y \)) increases by 1 foot.
The \( \frac{1}{2} \) part of the equation signifies the y-intercept, which indicates that when time (weeks) is zero (at the start), the sunflower's height is \( \frac{1}{2} \) foot.
So, the correct interpretation of the slope in this context is:
**The sunflower's height increases by an additional 1 foot each week.**