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?

The scatterplot shows the relationship between two variables, x and y. | SAT Two-variable data: Models and scatterplots Practice

Context: A scatterplot shows a decreasing trend. Near $x = 1$ , $y \approx 7$ ; near $x = 10$ , $y \approx 1$ .

Answer: $y = 8.7 - 0.8x$

Why: The data decreases, requiring negative slope. The $y$ -intercept extrapolates to about $8.7$ . Slope $\approx \dfrac{1 - 8.7}{10} = -0.8$ . Checking: at $x = 5$ , $y = 4.7$ (matches data $\approx 4$ – $5$ ).

Traps:

A ( $y = 0.8 + 8.7x$ ): Massive positive slope $8.7$ — completely wrong direction.
B ( $y = 0.8 - 8.7x$ ): Slope $-8.7$ is absurdly steep; $y$ -intercept $0.8$ is way too low.
C ( $y = 8.7 + 0.8x$ ): Good $y$ -intercept but positive slope contradicts the decreasing data.

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SAT Two-variable data: Models and scatterplots practice question

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