Linear Functions Flashcards

A linear function f satisfies f(0) = 4 and f(3) = 13. What is the equation of f?

Answer: f(x) = 3x + 4

Slope = (13 − 4)/(3 − 0) = 3; y-intercept = 4, so f(x) = 3x + 4.

What is the y-intercept of the line passing through (−2, 7) and (4, −5)?

Answer: 3

Slope = (−5 − 7)/(4 − (−2)) = −12/6 = −2; using point (4, −5): −5 = −2(4) + b → b = 3.

The linear function C(n) = 0.15n + 12 gives the monthly cost in dollars for n gigabytes of data used. What is the meaning of 12 in this context?

Answer: The fixed monthly base charge regardless of data used

In C(n) = 0.15n + 12, the constant 12 is the y-intercept — the cost when n = 0, meaning the base charge.

Line q passes through (1, −1) and is parallel to y = 4x + 7. What is the equation of line q?

Answer: y = 4x − 5

Parallel lines share slope 4; using (1, −1): −1 = 4(1) + b → b = −5, so y = 4x − 5.

If f(x) = ax + 6 and f(−2) = 0, what is the value of a?

Answer: 3

0 = a(−2) + 6 → −2a = −6 → a = 3.

A school raises money at $3.50 per ticket sold. The function R(t) = 3.50t models total revenue. How many tickets t must be sold to raise exactly $245?

Answer: 70

3.50t = 245 → t = 70.

What is the rate of change of the linear function described by the table? x: 2, 5, 8, 11 | y: 3, 12, 21, 30

Answer: 3

From x = 2 to x = 5, y increases from 3 to 12; slope = (12−3)/(5−2) = 9/3 = 3.

The equation of a line is 8x + 4y = 24. What is the slope of this line?

Answer: −2

Rewrite: 4y = −8x + 24 → y = −2x + 6; slope = −2.