To interpret the slope of the equation in the context of the growth of sunflowers, let's first clarify the equation given, which appears to be incomplete. Assuming a typical form for a linear equation of the line of best fit could be represented as:
\[ y = mx + b \]
Where:
- \( y \) is the height in feet (dependent variable),
- \( x \) is the independent variable which is related to time (in weeks),
- \( m \) is the slope,
- \( b \) is the y-intercept, representing the starting height when \( x = 0 \).
In the context provided, if \( x \) represents \( \frac{1}{2} \) times time in weeks, then our actual equation might be perceived in that context. The slope indicates how much the height of the sunflower (y) changes for each unit increase in the independent variable (time, which increases at \( \frac{1}{2} \) week intervals).
However, to answer the question specifically regarding the choices given about the slope, if we take one of the possible scenarios where the slope \( m = 1 \) (1 foot per each increase of 1 unit in time), then each increase in time (in \( \frac{1}{2} \) weeks) would indeed cause an increase in height.
Thus, interpreting the slope:
- If the slope is indeed 1 foot per \( \frac{1}{2} \) week, that would correspond to an increase of 2 feet for every full week that passes.
Given the options provided, C and D imply some confusion with units and terminology. However, since the model is also about the concept of measurement, the correct interpretation based on the context that the height increases can be derived from understanding that for every increment in time measured by the \( 1/2 x \), the effect is doubled when considered in full weekly context.
Therefore, the correct interpretation of the slope would be:
C: The sunflower's height increases by an additional 1 foot each week.