Linear Functions Flashcards

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.

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.

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.

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.

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.

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.

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.