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

The scatterplot shows the relationship between two variables, $x$ and $y$ .

Which of the following equations is the most appropriate linear model for the data shown?

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Explanation

Choice D is correct. The data points suggest that as the variable $x$ increases, the variable $y$ decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when $x$ is close to $0$ , $y$ is greater than $9$ . Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than $9$ . The graph of an equation of the form $y = a + b x$ , where $a$ and $b$ are constants, has a y-intercept with a y-coordinate of $a$ and has a slope of $b$ . Of the given choices, only choice D represents a graph that has a negative slope, $negative 0.9$ , and a y-intercept with a y-coordinate greater than $9$ , $9.4$ .

Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than $1$ , not greater than $9$ .

Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than $1$ , not greater than $9$ .

Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.