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?

Answer 1

In the given equation \( y = x + \frac{1}{2} \), which represents the line of best fit for the growth of sunflowers, the equation can be expressed in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

In this case, the slope \( m \) is equal to 1, and the y-intercept \( b \) is \( \frac{1}{2} \).

The slope of 1 means that for every additional week (for each unit increase in \( x \)), the height of the sunflower (the value of \( y \)) increases by 1 foot. Thus, the slope indicates the rate of growth of the sunflowers: they grow at a rate of 1 foot per week.

In summary, the slope of the line of best fit in this context signifies that the sunflowers grow 1 foot in height for every week of growth.