Answer:
option d.
Step-by-step explanation:
We have the following set of data:
x 0 1 2 3 4
f (x) 18 14 10 6 2
Let's assume the function is linear, then, the equation of the line would ne:
(y - y0) = m(x-x0)
where m= (y1-y0) / (x1-x0)
And (x1, y1) = (1, 14)
(x0, y0) = (0, 18)
You can choose any of the points given in the set of data.
Then,
m = (14-18)/(1-0) = -4.
Then the equation of the line is:
(y - 18) = -4x
y = -4x + 18.
If the function is linear, then all the points given in the set of data will satisfy the function. Let's try:
(2, 10):
10 = -4(2) + 18.
10 = 10
SATISFIES THE EQUATION
(3, 6):
6 = -4(3) + 18.
6 = 6
SATISFIES THE EQUATION
(4, 2)
2 = -4(4) + 18.
6 = 6
SATISFIES THE EQUATION
So, the function is linear. And the correct option is option d.
