Linear Functions Flashcards

A line with equation y = kx − 4 passes through the point (3, 8). What is the value of k?

Answer: 4

Substitute (3, 8): 8 = 3k − 4 → 3k = 12 → k = 4.

The rate of change of a linear function is 5 and f(2) = 11. What is f(0)?

Answer: 1

f(x) = 5x + b; 11 = 5(2) + b → b = 1, so f(0) = 1.

Line p is parallel to the line y = 3x − 7 and passes through (1, 2). What is the equation of line p?

Answer: y = 3x − 1

Parallel lines have equal slopes; using slope 3 and point (1, 2): 2 = 3(1) + b → b = −1, so y = 3x − 1.

A cell phone plan charges a monthly base fee of $25 plus $0.10 per text message. If a customer's bill is $37, how many text messages did they send?

Answer: 120

25 + 0.10t = 37 → 0.10t = 12 → t = 120 text messages.

The graph below has a y-intercept of 4 and passes through (2, 0). What is the slope of the line?

Answer: −2

Slope = (0 − 4)/(2 − 0) = −4/2 = −2.

If f is a linear function and f(−1) = 7 and f(3) = −1, what is f(1)?

Answer: 3

Slope = (−1 − 7)/(3 − (−1)) = −8/4 = −2; using f(−1) = 7: 7 = −2(−1) + b → b = 5; f(1) = −2(1) + 5 = 3.

In the equation y = 2x + c, the line passes through the origin. What is the value of c?

Answer: 0

Passing through the origin means (0, 0) is on the line; 0 = 2(0) + c → c = 0.