Question

which of the following equations is the most appropriate linear model for the data shown in the scatterplot? 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:

Step1: Analyze the slope

The scatterplot shows a negative correlation (as x increases, y decreases), so the slope should be negative. This eliminates options C ($y = 1.9x - 10.1$) and D ($y = 1.9x + 10.1$) since their slopes are positive.

Step2: Analyze the y - intercept

For a linear equation $y = mx + b$, when $x = 0$, $y=b$. Looking at the scatterplot, when $x = 0$, the y - value should be around 10 (since the first point is near (0,9 - 10)). Let's check the y - intercepts of the remaining options. Option A: $y=-1.9x - 10.1$ has a y - intercept of - 10.1 (which is negative, not matching the graph). Option B: $y=-1.9x + 10.1$ has a y - intercept of 10.1 (positive, which matches the general position of the data at $x = 0$). Also, the slope of - 1.9 indicates a negative trend, which matches the scatterplot.

Answer:

B. $y = -1.9x + 10.1$