Linear Functions Flashcards

A candle is 18 cm tall and burns at 0.6 cm per minute. The function h(t) = 18 − 0.6t models its height. After how many minutes will it be 7.2 cm tall?

Answer: 18

18 − 0.6t = 7.2 → 0.6t = 10.8 → t = 18.

Line r is perpendicular to y = (3/4)x − 2. Which equation could represent line r?

Answer: y = −(4/3)x + 5

The perpendicular slope is the negative reciprocal of 3/4, which is −4/3; y = −(4/3)x + 5 has that slope.

If g(x) = −3x + 7, for what value of x does g(x) = g(−1)?

Answer: −1

g(−1) = −3(−1) + 7 = 10; g(x) = 10 → −3x + 7 = 10 → −3x = 3 → x = −1. The function value g(−1) equals itself only at x = −1.

Two lines intersect at (3, 5). One line has equation y = x + 2. Which of the following could be the other line's equation?

Answer: y = −2x + 11

Check: −2(3) + 11 = −6 + 11 = 5 ✓; (3, 5) lies on y = −2x + 11.

What does the x-intercept of a linear function represent in a context where y is profit (in dollars) and x is units sold?

Answer: The break-even point — the number of units where profit equals zero

The x-intercept is where profit y = 0, meaning the number of units at which the business neither gains nor loses money — the break-even point.

The table below shows a linear function. What is the missing value? x: −1, 0, 1, 2 | y: −5, −2, 1, ?

Answer: 4

The rate of change is 3 per unit; continuing from y = 1 at x = 1: y = 1 + 3 = 4.

A swimmer starts 200 meters from a dock and swims toward it at 2.5 meters per second. Which function models distance d from the dock after t seconds?

Answer: d(t) = 200 − 2.5t

Starting at 200 m and decreasing at 2.5 m/s gives d(t) = 200 − 2.5t.

For f(x) = 5x − 9 and g(x) = 3x + 1, what is the x-value where f(x) = g(x)?

Answer: 5

5x − 9 = 3x + 1 → 2x = 10 → x = 5.