SAT Scatterplots: Predict a Value from a Linear Model

A data table contains the pairs (1, 9), (2, 13), (3, 17), and (4, 21). A linear model fits these pairs exactly. According to the model, what is y when x = 6?

Calculate the constant rate

Every increase of 1 in x raises y by 4. The slope is m = 4.

Find the intercept

Use (1,9) in y = 4x + b: 9 = 4 + b, so b = 5. The model is y = 4x + 5.

Evaluate the model

At x = 6, y = 4(6) + 5 = 29. The prompt asks for a model prediction, not an observed data value.

Enter the data in Desmos columns x₁ and y₁, then type y_1 ~ m x_1 + b. The exact data yield m = 4 and b = 5. Defining f(x) = 4x + 5 and evaluating f(6) gives 29. Check this against the hand calculation.

• 24 uses the slope but omits the intercept.
• 25 is the model value at x = 5.
• 33 is the model value at x = 7.

For this model, what is the predicted difference in y between x = 6 and x = 8?

Answer: 8

The change in x is 2. Multiply by the slope: Δy = 4 × 2 = 8. Equivalently, 37 − 29 = 8.

If this was difficult, return to scatterplots practice and identify the precise step to improve. These are original PeakSAT teaching examples, not official College Board questions or calibrated score predictions. For official adaptive test practice, use Bluebook (opens in a new tab).