Linear functions

Question 1

slope of a line

Answer 1

the slope 𝑚 of the line containing points P(a, b) and Q(c, d) is

𝑚 = (d – b)/(c – a)

Question 2

a line with positive slope is

Answer 2

increasing

Question 3

a line with negative slope is

Answer 3

decreasing

Question 4

a line with 0 slope is

Answer 4

horizontal (constant)

Question 5

a line with undefined slope is

Answer 5

vertical

Question 6

point-slope form of a line

Answer 6

the point-slope form of a line with slope m containing the point (x₀, y₀) is

y – y₀ = m(x – x₀)

Question 7

slope-intercept form of a line

Answer 7

the slope intercept-form of a line with slope m and y-intercept (0, b) is

y = mx + b

Question 8

linear function

Answer 8

a function of the form f(x) = mx + b, where m and b are real numbers with m ≠ 0

Question 9

domain of a linear function

Answer 9

(–∞, ∞)

Question 10

constant function

Answer 10

a function of the form f(x) = b, where b is a real number

Question 11

domain of a constant function

Answer 11

(–∞, ∞)

Question 12

average rate of change

Answer 12

the average rate of change of a function f, defined on the interval [a, b], is

Δf/Δx = [f(b) – f(a)]/(b – a)