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?

A. m = 2
B. m = 3
C. m = 19
D. m = 35

Which is the correct answer???

Answer 1

19...................................

Answer 2

Answer: The correct option is (C) 19.

Step-by-step explanation: We are given to find the value of m so that the data the table to represent a linear function with a rate of change of –8.

We know that

the rate of change for a linear function with two points (a, b) and (c, d) is given by

`R=(d-b)/(c-a).`

From the table, we note that the points (10, 27) and (11, m) satisfy the given linear function.

So, the rate of change of the linear function will be

`R=(m-27)/(11-10)\\\\\\\Rightarrow -8=(m-27)/(1)\\\\\Rightarrow -8=m-27\\\\\Rightarrow m=27-8\\\\\Rightarrow m=19.`

Thus, the required value of m is 19.

Option (C) is CORRECT.