Final answer is The best approximation for the cost of an additional square foot of living space for homes in this neighborhood is $5333.33.
The scatterplot shows the relationship between the cost, C, in thousands of dollars, and the living space, x, in square feet. To estimate the cost for an additional square foot of living space, we can find the slope of the line of best fit for the scatterplot. The slope represents the rate of change of the cost with respect to the living space.
We can calculate the slope by finding the difference in the cost for two different values of living space and dividing it by the difference in the living space. Let's choose two points from the scatterplot and calculate the slope:
Choose a point A: (x1, C1) at coordinates (35, 300) with living space x1 = 35 ft^2 and cost C1 = 300000 dollars.
Choose a point B: (x2, C2) at coordinates (50, 380) with living space x2 = 50 ft^2 and cost C2 = 380000 dollars.
Calculate the difference in cost: C2 - C1 = 380000 - 300000 = 80000 dollars.
Calculate the difference in living space: x2 - x1 = 50 - 35 = 15 ft^2.
Calculate the slope: slope = (C2 - C1) / (x2 - x1) = 80000 / 15 = 5333.33 dollars per square foot.
The best approximation for the cost of an additional square foot of living space is $5333.33. Therefore, none of the provided options (1. $80, 2. $300, 3. $1,000, 4. $13,000) are accurate.