Question

which scatterplot most likely has a line of best fit represented by $y = -2x + 1$

Explanation:

Step1: Analyze the slope and y-intercept

The equation of the line is \( y = -2x + 1 \). The slope (\( m \)) is -2 (negative, so the line should be decreasing from left to right) and the y-intercept (\( b \)) is 1 (the line crosses the y-axis at \( (0,1) \)).

Step2: Evaluate each scatterplot

• For a scatterplot to have this line of best fit, the points should show a negative linear trend (since slope is negative) and the general trend should align with a line that has a steep negative slope (slope of -2 is relatively steep) and crosses the y-axis near 1. We need to look for the scatterplot where the points are roughly following a line that is decreasing steeply and has a y-intercept around 1.

Assuming the scatterplots are labeled X, Y, W, Z, and one of them has points that trend downwards (negative slope) with a steepness consistent with slope -2 and y-intercept around 1. Let's assume the correct one (for example, if we visualize typical scatterplots: a line with slope -2 is steeply decreasing, so the scatterplot with points going down from left to right, steeper than a slope of -1, and crossing y-axis near 1 would be the one. Suppose the correct option is, say, X (but this depends on the actual scatterplots, but following the analysis of the line's properties: negative slope, steep, y-intercept 1).

Answer:

(Assuming the correct scatterplot is, for example, X. But since the actual scatterplots are not fully visible, but based on the line \( y = -2x + 1 \) (negative slope, steep, y-intercept 1), the scatterplot with points showing a steep negative trend and y-intercept near 1. If we take the options as given, and assuming the correct one is, say, X (but this needs the actual plots, but following the line's equation, the answer would be the scatterplot with negative steep trend and y-intercept ~1. So if the options are X, Y, W, Z, and the correct one is, for example, X, then the answer is X. But since the user's image has four options, and the line is \( y=-2x + 1 \), the correct scatterplot is the one with negative slope (decreasing) and steep (slope -2) and y-intercept 1. So the answer would be the option (e.g., X) that matches this. )

(Note: Since the actual scatterplots are not fully detailed, but based on the line's equation, the key is negative slope (decreasing), steep (slope -2), y-intercept 1. So the scatterplot with points trending down steeply and crossing y-axis near 1 is the answer. If we assume the correct option is, say, X (depending on the actual plots), but the process is to check slope (negative, steep) and y-intercept (1).)