Linear Functions Flashcards

Which of the following equations represents a linear function?

Answer: y = 3x + 2

y = 3x + 2 is the only equation of the form y = mx + b, making it linear.

The function R(x) = −2x + 14 models the remaining miles x days into a road trip. On what day will 4 miles remain?

Answer: 5

−2x + 14 = 4 → −2x = −10 → x = 5.

A linear function f has the equation f(x) = px − 8. If f(4) = 4, what is the value of p?

Answer: 3

4p − 8 = 4 → 4p = 12 → p = 3.

Line m passes through (2, 5) and is perpendicular to a line with slope −1/3. What is the equation of m?

Answer: y = 3x − 1

Perpendicular slope = 3; using (2, 5): 5 = 3(2) + b → b = −1; y = 3x − 1.

The points (1, a) and (4, 13) lie on a line with slope 2. What is the value of a?

Answer: 7

(13 − a)/(4 − 1) = 2 → 13 − a = 6 → a = 7.

A line passes through the origin and the point (5, −15). Which equation represents this line?

Answer: y = −3x

Slope = (−15 − 0)/(5 − 0) = −3; passes through origin means y-intercept = 0: y = −3x.

In the linear equation 4y − 3x = 8, what is the x-intercept?

Answer: (−8/3, 0)

Set y = 0: −3x = 8 → x = −8/3; x-intercept is (−8/3, 0).

f(x) = 6x − 4 and h is a linear function parallel to f with h(0) = 7. What is h(3)?

Answer: 25

Parallel to f means same slope 6; h(0) = 7 means y-intercept = 7; h(3) = 6(3) + 7 = 25.