Question

Here is the question. These are the answer choices A; Yes, because it has a constant rate of change. B; Yes, because it does not have a constant rate of change.C; No, because it has a constant rate of change.D; No, because is does not have a constant rate of change.

Answer 1

the linear function has the form:

y = mx + c

where m is the rate of change and c is constant

to find m and c, substitute with x and y from the table

if x = 6 , y = 4

so, 4 = 6m + c (1)

and if x = 8 , y = 0

so, 0 = 8m + c (2)

from (2)

c = -8m (3)

from (3) and at (1)

4 = 6m - 8m

so, 4 = -2m

m = 4/-2 = -2

c = -8 * -2 = 16

y = -2x + 16

now substitute with x = 7

y = -2 * 7 + 16 = -14 + 16 = 2 which agree with the value from the table

and when x = 9

y = -2 * 9 + 16 = -18 + 16 = -2 which agree with the value from the table

so, the function is linear

so, the last answer of the question, is the function non-linear?

C: No, because it has a constant rate of change.

the answer is option C