do this values in the table represent a linear function? If so what is the function rule?

X -2. 0. 2. 4
Y -4. 0. 4. 8

A) the values do not show linear function
B) yes they show y=1/2x+4
C) yes they show y=2x+2
D) yes they show y=2x
My answer: C or D?

Did you check if the slope between any two points is always the same ?

Hint: the point (0,0) is a good point to check in the given equations.
Which equation does it satisfy ?

Ohhhh okay. So it's D

To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the values of x and y.

Looking at the given values:

x: -2, 0, 2, 4
y: -4, 0, 4, 8

We can see that as x increases by 2 units, y also increases by 4 units. This consistent rate of change indicates that a linear function is present.

To find the function rule, we can calculate the slope (m) by using the formula:

m = (change in y) / (change in x)

In this case, the change in y = 4, and the change in x = 2, so:

m = 4 / 2
m = 2

Therefore, the function rule for the table is:

y = 2x

So, the correct answer would be D) Yes, they show y=2x.

To determine whether the values in the table represent a linear function, we need to check whether the ratio of the change in Y to the change in X remains constant.

Let's calculate the difference between consecutive Y values and the difference between consecutive X values:

Difference in Y:
0 - (-4) = 4
4 - 0 = 4
8 - 4 = 4

Difference in X:
0 - (-2) = 2
2 - 0 = 2
4 - 2 = 2

As we can see, the ratio of the change in Y to the change in X is always 4/2 = 2. This implies that the values in the table represent a linear function.

To find the function rule, we can now determine the value of the y-intercept and the slope using any of the given options. Let's plug in the first pair of X and Y values (-2, -4) into the given options and see which one fits:

A) y = 1/2x + 4:
-4 = 1/2(-2) + 4
-4 = -1 + 4
-4 = 3 (not true)

B) y = 2x + 2:
-4 = 2(-2) + 2
-4 = -4 + 2
-4 = -2 (not true)

C) y = 2x + 2:
-4 = 2(-2) + 2
-4 = -4 + 2
-4 = -2 (not true)

D) y = 2x:
-4 = 2(-2)
-4 = -4 (true)

From the calculations, we can see that option D) y = 2x is the correct function rule.