The scatterplot shows the relationship between two variables, and .
- The scatterplot has 10 data points.
- The data points are in a linear pattern trending down from left to right.
- The data points have the following approximate coordinates:
- (0 comma 10)
- (1.2 comma 9)
- (2.3 comma 8)
- (3.1 comma 5)
- (4.8 comma 5)
- (5.2 comma 3)
- (6.5 comma 3)
- (7.2 comma 3)
- (9.6 comma 2)
- (8.8 comma 1)
Which of the following equations is the most appropriate linear model for the data shown?
Correct answer: D
Explanation
Choice D is correct. The data points suggest that as the variable increases, the variable decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when is close to , is greater than . Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than . The graph of an equation of the form , where and are constants, has a y-intercept with a y-coordinate of and has a slope of . Of the given choices, only choice D represents a graph that has a negative slope, , and a y-intercept with a y-coordinate greater than , .
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 , not greater than .
Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than , not greater than .
Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.
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