Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?
Correct answer: B. y = -1.9x + 10.1
- A. y = -1.9x - 10.1
- B. y = -1.9x + 10.1
- C. y = 1.9x - 10.1
- D. y = 1.9x + 10.1
Explanation
Choice B is correct. The equation representing a linear model can be written in the form y = a + bx , or y = bx + a, where b is the slope of the graph of the model and (0,a) is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b<0. The scatterplot also shows that the data points are close to the y-axis at a positive value of y . Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means a>0. Of the given choices, only choice B, y = -1.9x + 10.1 has a negative value for b, the slope, and a positive value for a, the y-coordinate of the y-intercept.
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