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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Easy

The scatterplot shows the relationship between $x$ and $y$ . A line of best fit is also shown.

Which of the following is closest to the slope of the line of best fit shown?

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Explanation

Choice C is correct. It's given that the scatterplot shows the relationship between two variables, $x$ and $y$ , and a line of best fit is shown. For the line of best fit shown, for each increase in the value of $x$ by $1$ , the corresponding value of $y$ increases by a constant rate. It follows that the relationship between the variables $x$ and $y$ has a positive linear trend. A line in the xy-plane that passes through the points $(a, b)$ and $(c, d)$ has a slope of $\frac{d - b}{c - a}$ . The line of best fit shown passes approximately through the points $left parenthesis 0 comma 0.25 right parenthesis$ and $left parenthesis 4 comma 2 right parenthesis$ . It follows that the slope of this line is approximately $\frac{2 - 0.25}{4 - 0}$ , which is equivalent to $0.4375$ . Therefore, of the given choices, $0.44$ is closest to the slope of the line of best fit shown.

Choice A is incorrect. This is the slope of a line of best fit for a relationship between $x$ and $y$ that has a negative, rather than a positive, linear trend.

Choice B is incorrect. This is the slope of a line of best fit for a relationship between $x$ and $y$ that has a negative, rather than a positive, linear trend.

Choice D is incorrect and may result from conceptual or calculation errors.