Question

the table shows the relationship between square footage and rent prices for different locations.
what does the slope say about the data? use the linear regression calculator to find the slope.
the slope indicates that rent doubles as square footage increases, reflecting a high premium on larger properties.
the slope indicates no clear trend between square footage and rent, suggesting that factors other than size may influence rent costs.
the slope indicates that as the square footage increases, the rent increases proportionally, demonstrating a direct correlation between size and cost.

Explanation:

Step1: Calculate the slope using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Let's take two points \((x_1,y_1)=(600,850)\) and \((x_2,y_2)=(800,1300)\)

$$m=\frac{1300 - 850}{800 - 600}=\frac{450}{200}=2.25$$

Step2: Analyze the meaning of the slope

The slope \(m = 2.25\) means that for every 1 - unit increase in square footage (\(x\)), the rent (\(y\)) increases by \(2.25\). So, as the square footage increases, the rent increases proportionally, demonstrating a direct correlation between size and cost.

Answer:

The slope indicates that as the square footage increases, the rent increases proportionally, demonstrating a direct correlation between size and cost.