The scatterplot shows the relationship between two variables, and . Which equation is the most appropriate linear model for this relationship?

Solution available with step-by-step explanation

SAT Two-Variable Data Question 10 | Free SAT Prep | Aniko

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Question 10·Easy·Two-Variable Data: Models and Scatterplots

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The scatterplot shows the relationship between two variables, $x$ and $y$ .

Which equation is the most appropriate linear model for this relationship?

For a scatterplot linear-model question, first determine whether the trend is increasing or decreasing to eliminate slopes with the wrong sign. Then estimate the slope using two points that are far apart, and pick the equation whose slope is closest to that estimate.

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Check the direction

Decide whether the pattern goes up or down as $x$ increases.

Estimate rise over run

Pick two plotted points that are far apart and estimate the slope (change in $y$ divided by change in $x$ ).

Match the slope

Choose the equation whose slope is closest to your estimate.

Desmos Guide

Graph each candidate line

Enter $y=3x+2$ , $y=x+2$ , $y=-2x+2$ , and $y=2x+2$ .

Compare to the plotted points

Check which line stays closest to the cluster of points (for instance, compare how each line fits near $x=1$ and near $x=5$ ).

Select the best-fitting line

Choose the line that best matches the overall upward trend of the points across the full range of $x$ .

Step-by-step Explanation

Estimate the slope from the scatterplot

Using two points that are far apart, such as $(1,4)$ and $(5,11)$ , the slope is approximately

\frac{11-4}{5-1}=\frac{7}{4}=1.75,

which is closest to 2 among the choices.

Choose the equation with the closest slope

All the choices have a $y$ -intercept of 2, so the best model is the one whose slope best matches the trend. Therefore, the most appropriate model is $y = 2x + 2$ .

Strategy

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Step-by-step Explanation

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Strategy

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Step-by-step Explanation