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Linear Functions 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.

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  1. A company's weekly profit P (in dollars) is modeled by P(u) = 45u − 360, where u is the number of units sold. How many units must be sold for the company to break even (P = 0)?

    Answer: 8

    Set P = 0: 45u − 360 = 0 → 45u = 360 → u = 8 units.

  2. If f(x) = −5x + 2 and g(x) = 3x − 6, for what value of x does f(x) = g(x)?

    Answer: 1

    −5x + 2 = 3x − 6 → 8 = 8x → x = 1.

  3. The linear model T = 0.9F − 17.8 converts a temperature in degrees Fahrenheit (F) to a temperature in Celsius (T). Approximately what Fahrenheit temperature corresponds to 0°C?

    Answer: 20°F

    Set T = 0: 0 = 0.9F − 17.8 → 0.9F = 17.8 → F ≈ 19.8 ≈ 20°F.

  4. Point A is at (0, 3) and point B is at (6, 0). What is the length of segment AB?

    Answer: 3√5

    AB = √((6−0)² + (0−3)²) = √(36 + 9) = √45 = 3√5.

  5. A linear function f has the following values: f(1) = 4 and f(4) = 13. What is the slope of f?

    Answer: 3

    Slope = (13 − 4)/(4 − 1) = 9/3 = 3.

  6. Which equation represents a line that passes through (2, −3) with slope 1/2?

    Answer: y = (1/2)x − 4

    Using point-slope form: y − (−3) = (1/2)(x − 2) → y = (1/2)x − 1 − 3 = (1/2)x − 4.

  7. For the linear function shown in the table, what is the missing value? x: 1 2 3 4 f: 6 9 12 ?

    Answer: 15

    The common difference is 3, so f(4) = 12 + 3 = 15.