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Two-Variable Data: Models and Scatterplots Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Two-Variable Data: Models and Scatterplots flashcards as text

  1. A linear model for daily temperature (x, °F) and swimming pool attendance (y, people) is y = 5x − 150. On what temperature day does attendance equal 100 people?

    Answer: 50°F

    Set 100 = 5x−150 → 5x=250 → x=50.

  2. Data shows sales (y) in thousands grow as y = 8(1.2)^x. After 3 years (x=3), what are predicted sales?

    Answer: 13.824 thousand

    y = 8(1.2)^3 = 8 × 1.728 = 13.824 thousand.

  3. In a scatterplot, a point has a large positive residual. What does this mean?

    Answer: The actual y value is much higher than the model predicted.

    Residual = actual y − predicted y; a large positive residual means actual y >> predicted y.

  4. The line of best fit for data on advertising (x, $000) and revenue (y, $000) passes through (2, 50) and (8, 80). What is the slope?

    Answer: 5

    Slope = (80−50)/(8−2) = 30/6 = 5.

  5. A model y = kx² fits a dataset. When x = 3, y = 36. What is the value of k?

    Answer: 4

    36 = k(9) → k = 36/9 = 4.

  6. A scatterplot of income (x) and spending (y) has a line of best fit y = 0.75x + 500. A household earns $4,000. What does the model predict for spending?

    Answer: $3,500

    y = 0.75(4000)+500 = 3000+500 = 3500.

  7. A scatterplot shows data with no discernible pattern — points are randomly scattered. What is the approximate value of r?

    Answer: r ≈ 0

    No pattern in a scatterplot corresponds to little or no linear association, so r ≈ 0.