Question

In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m?

m = 2
m = 3
m = 19
m = 35

Answer 1

a rate of change of –8
so
27 - 8 = 19
19 - 8 = 11

answer

m = 19

Answer 2

m= 19

Explanation:

In a linear function the rate of change of y-variable respect x-variable must be constant. In mathematical terms:

Δy/Δx = constant

Given two points of the function: (x1, y1) and (x2, y2), Δy = (y2 -y1) and Δx = (x2 -x1). So,

Δy/Δx = (11 -27)/(12-10) = -8

(m -27)/(11-10) = -8

(m -27) = -8*(11-10)

m = -8 + 27

m = 19