One of Robert’s homework problems had the following function table.

x | y
0 | 4
2 | 8
4 | 12
6 | 16

Robert concluded that the rule for this function table was y =2x + 4.
Which statement best justifies that Robert’s conclusion is correct?

A. The x-values are all even numbers and 2 is an even number.
B. The y-intercept of the equation is 4 and the first point is (0, 4).
C. Each x-value put into the equation yields the corresponding y-value.
D. All the x-values are positive, so all the y-values will also be positive.

Surely, C

They are all true, but that does not mean that they justify using that equation for that table. C is the right choice, because every entry in the table matches the equation.

You could have x=2, y=4 which would satisfy A, but not the equation.
B is true for any line going through (0,4), not just the line for this equation
D (see A)

Sir obleck please how where you able to justify and stand by your answer C?

All of the options are true to me....I was deeply Wondering

I need your explanation

Oh yes yes I see thank you very much

To justify Robert's conclusion that the rule for this function table is y = 2x + 4, we need to evaluate each of the given options.

Option A: The fact that the x-values are all even numbers and 2 is an even number does not directly confirm the validity of Robert's conclusion. It is not necessary for the x-values and coefficients in the equation to be of the same parity for the equation to be true.

Option B: This justifies the y-intercept of the equation, which is 4, but it does not prove that the equation holds true for all the points in the function table.

Option C: This statement is the strongest justification for Robert's conclusion. If each x-value put into the equation yields the corresponding y-value, it confirms the rule y = 2x + 4 for this function table. An example of this is when x = 0, y = 2(0) + 4 = 4, which matches the first point in the table (0, 4).

Option D: The fact that all the x-values are positive does not guarantee that all the y-values will also be positive. The equation can still hold true even if the y-values are negative when the x-values are positive.

Therefore, the best justification for Robert's conclusion is option C: Each x-value put into the equation yields the corresponding y-value.