Question

which of the following is the best interpretation of the slope of the line of best fit in this context?
a the number of tomato seeds planted is predicted to increase by 60 seeds every 100 days.
b the number of tomato seeds planted is predicted to increase by 300 seeds every 100 days.
c the number of tomato seeds that germinate is predicted to increase by 60 seeds for every additional 100 tomato seeds that are planted.
d the number of tomato seeds that germinate is predicted to increase by 300 seeds for every additional 100 tomato seeds that are planted.

Explanation:

Step1: Understand the concept of slope in regression

In a regression line \(y = mx + b\) (where \(y\) is the dependent variable - number of germinated seeds, \(x\) is the independent variable - number of planted seeds), the slope \(m=\frac{\Delta y}{\Delta x}\).

Step2: Analyze the units and relationship

The slope represents the change in \(y\) (number of germinated seeds) per unit change in \(x\) (number of planted seeds). If we consider a change in \(x\) of \(100\) units (number of planted seeds), and assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line of best - fit such that \(x_2 - x_1=100\). From the graph (by visual inspection of the trend of the line of best - fit), the change in \(y\) (number of germinated seeds) \(\Delta y=y_2 - y_1 = 60\). So the slope interpretation is that for every additional 100 tomato seeds planted (\(\Delta x = 100\)), the number of germinated seeds (\(y\)) increases by 60 (\(\Delta y=60\)).

• Option A and B are wrong because they talk about the number of planted seeds increasing over time (not the relationship between planted and germinated seeds).
• Option D is wrong because the slope value (from the trend of the line, for \(\Delta x = 100\), \(\Delta y

eq300\)).

Answer:

C. The number of tomato seeds that germinate is predicted to increase by 60 seeds for every additional 100 tomato seeds that are planted.