Question

Is the function represented by the table linear or nonlinear and why? X- 2,4,6,8 Y- 10,9,8,7 A) the function is linear because all of the values on the table are positive B) the function is not linear because there is no x-value of 0 C) the function is linear because it decreases at a constant rate D) the function is not linear because the x- values and y-values are increasing in opposite directions

Answer 1

the answer is C. It is decreasing at a constant rate

Answer 2

C) the function is linear because it decreases at a constant rate

Explanation:

X- 2,4,6,8

Y- 10,9,8,7

To check whether the given function is linear or not linear , we need to check the difference of x and y values. we take (x,y)

(2,10) and (4,9)

We find out the slope

`slope = (y_2-y_1)/(x_2-x_1)=(9-10)/(4-2)= -0.5`

Like that we find the slope using another two points

(6,8) and (8,7)

We find out the slope

`slope = (y_2-y_1)/(x_2-x_1)=(7-8)/(8-6)= -0.5`

We got the same slope

So , function is linear.

Also we got slope = -0.5 that means the function decreases at a constant rate