Linear Functions Flashcards

Line s passes through (−4, 3) and (0, −1). What is the equation of line s?

Answer: y = −x − 1

Slope = (−1 − 3)/(0 − (−4)) = −4/4 = −1; y-intercept = −1, so y = −x − 1.

A linear model predicts that every additional hour of study increases a test score by 4 points, starting from a base of 58. Which equation represents score S after h hours?

Answer: S = 4h + 58

The rate of increase is 4 per hour (slope = 4) and the initial score is 58 (y-intercept), giving S = 4h + 58.

If f(3) = 11 and the rate of change is −3, what is f(6)?

Answer: 2

From x = 3 to x = 6 is 3 steps; f(6) = 11 + 3(−3) = 11 − 9 = 2.

Which line has an undefined slope?

Answer: x = 7

A vertical line such as x = 7 has undefined slope because the change in x is zero.

The function P(w) = 80w − 320 gives weekly profit P in dollars when w workers are employed. How many workers are needed to break even?

Answer: 4

P(w) = 0 → 80w = 320 → w = 4.

A line has a slope of 2/5 and passes through (5, 4). What is the y-intercept?

Answer: 2

4 = (2/5)(5) + b → 4 = 2 + b → b = 2.

At time t = 0, a train is 15 miles from a station. It travels away at 60 mph. Which function gives its distance D from the station?

Answer: D(t) = 60t + 15

Starting 15 miles away and moving at 60 mph further away: D(t) = 60t + 15.

What is the value of k if the points (k, 1) and (3, 7) lie on a line with slope 3?

Answer: 1

Slope = (7 − 1)/(3 − k) = 3 → 6 = 3(3 − k) → 6 = 9 − 3k → 3k = 3 → k = 1.