Linear Functions Flashcards

A truck travels at a constant speed. After 2 hours it has traveled 110 miles, and after 5 hours it has traveled 275 miles. How many miles per hour is the truck traveling?

Answer: 55 mph

Rate = (275 − 110)/(5 − 2) = 165/3 = 55 mph.

Which line is perpendicular to y = (2/3)x + 1?

Answer: y = −(3/2)x + 5

Perpendicular slopes are negative reciprocals; the negative reciprocal of 2/3 is −3/2, giving y = −(3/2)x + 5.

A linear function f satisfies f(0) = −6 and f(4) = 10. What is f(6)?

Answer: 18

Slope = (10 − (−6))/(4 − 0) = 16/4 = 4; f(x) = 4x − 6; f(6) = 24 − 6 = 18.

In the function P(t) = 1200 − 40t, P represents the number of gallons of water in a pool and t represents time in hours. What does −40 represent?

Answer: The rate at which water drains (40 gallons per hour)

The coefficient of t (slope) = −40 represents the rate of change: water decreases by 40 gallons each hour.

If the equation of a line is written as 6x − 2y = 8, what is the slope of the line?

Answer: 3

Rewrite in slope-intercept form: −2y = −6x + 8 → y = 3x − 4, so the slope is 3.

The function C(x) = 0.08x + 15 represents the monthly cost (in dollars) of a streaming service, where x is the number of premium channels added. If a customer pays $23.40, how many premium channels did they add?

Answer: 105

0.08x + 15 = 23.40 → 0.08x = 8.40 → x = 105.

A line ℓ has slope −3 and passes through (2, 7). Which point also lies on line ℓ?

Answer: (0, 13)

Equation: y − 7 = −3(x − 2) → y = −3x + 13; at x = 0, y = 13. Checking (0, 13): 13 = −3(0) + 13 ✓.