In the equation \( y = x + 32 \), the slope of the line (the coefficient of \( x \)) is 1. This means that for each additional week (increase of 1 in \( x \)), the height of the sunflower (increase of \( y \)) increases by 1 foot.
Therefore, the correct response is:
The sunflower's height increases by an additional 1 foot each week.