Linear Functions Flashcards

Line n is defined by 3x + 6y = 18. What is the slope of a line perpendicular to n?

Answer: 2

Rewrite: y = −(1/2)x + 3; slope of n = −1/2; perpendicular slope = 2.

A function is linear if and only if it has a constant rate of change. Which of the following tables is linear? A: x=1,2,3,4; y=2,6,12,20 | B: x=0,2,4,6; y=1,5,9,13 | C: x=1,3,5,7; y=3,9,27,81 | D: x=0,1,2,3; y=4,3,1,−2

Answer: B

Table B has a constant rate of change: +4 per +2 units in x (slope = 2). The others have non-constant rates.

If f(x) = 4x + b and f(2) = 11, what is f(−1)?

Answer: −1

f(2) = 8 + b = 11 → b = 3; f(−1) = −4 + 3 = −1.

The graph of a linear function has a slope of 0 and passes through (2, −5). Which is the equation?

Answer: y = −5

A slope of 0 means a horizontal line; passing through (2, −5) gives y = −5.

A savings account starts with $300 and earns $25 per week. How many weeks w until the account reaches $700?

Answer: 16

300 + 25w = 700 → 25w = 400 → w = 16.

What is the difference in y-intercepts between the lines y = 3x + 7 and y = 3x − 4?

Answer: 11

Y-intercepts are 7 and −4; 7 − (−4) = 11.

The function d(t) = 65t + 10 gives the distance (in miles) a car has traveled t hours after a road trip began, where 10 miles had already been covered. What does 65 represent?

Answer: The speed of the car in miles per hour

In d(t) = 65t + 10, the coefficient 65 is the slope — the rate at which distance increases per hour, i.e., the speed.

Line j passes through (−3, 0) and has slope 2. Which point also lies on line j?

Answer: (0, 6)

Equation: y = 2(x + 3) = 2x + 6; at x = 0, y = 6. So (0, 6) is on the line.