Question

Complete the table.
x
0
1
2
3
4
5
y
0
9
18
  
27
  
36
  
45
Part 2
The table shows the relationship between x and y. Which statement expresses that​ relationship?
A.
Each value of y is 8 times the corresponding value of x.
B.
Each value of y is 8 greater than the corresponding value of x.
C.
Each value of y is 9 times the corresponding value of x.
D.
Each value of y is 9 greater than the corresponding value of x.

Answer 1

Let's first complete the table. The values provided are as follows:

| x | y |
|---|----|
| 0 | 0 |
| 1 | 9 |
| 2 | 18 |
| 3 | |
| 4 | |
| 5 | |

To find the missing values of y:

For \(x = 3\):
From the pattern we see that \(y\) increases by 9 for each increment of 1 in \(x\). Therefore, when \(x = 3\):
\[
y = 18 + 9 = 27
\]

For \(x = 4\):
When \(x = 4\):
\[
y = 27 + 9 = 36
\]

For \(x = 5\):
When \(x = 5\):
\[
y = 36 + 9 = 45
\]

Completing the table gives us:

| x | y |
|---|----|
| 0 | 0 |
| 1 | 9 |
| 2 | 18 |
| 3 | 27 |
| 4 | 36 |
| 5 | 45 |

Now we need to express the relationship between \(x\) and \(y\).

From the table, we can see that each value of \(y\) corresponds to the formula:
\[
y = 9x
\]

Which matches with statement C: "Each value of y is 9 times the corresponding value of x."

Therefore, the correct answer is:
**C. Each value of y is 9 times the corresponding value of x.**