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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

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

Answer:

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

Step-by-step 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

[tex]slope = \frac{y_2-y_1}{x_2-x_1}=\frac{9-10}{4-2}= -0.5[/tex]

Like that we find the slope using another two points

(6,8)  and (8,7)

We find out the slope

[tex]slope = \frac{y_2-y_1}{x_2-x_1}=\frac{7-8}{8-6}= -0.5[/tex]

We got the same slope

So , function is linear.

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



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