Let's determine which table satisfies the equation [tex]\( y = -2 + 4x \)[/tex].
### Table 1
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|---------|---------|
| -5 | -22 |
| 0 | -2 |
| 3 | 10 |
Let's check each pair:
For [tex]\( x = -5 \)[/tex]:
[tex]\[
y = -2 + 4(-5) = -2 - 20 = -22
\][/tex]
The value matches [tex]\( y = -22 \)[/tex].
For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -2 + 4(0) = -2 + 0 = -2
\][/tex]
The value matches [tex]\( y = -2 \)[/tex].
For [tex]\( x = 3 \)[/tex]:
[tex]\[
y = -2 + 4(3) = -2 + 12 = 10
\][/tex]
The value matches [tex]\( y = 10 \)[/tex].
Since all values in Table 1 satisfy the equation [tex]\( y = -2 + 4x \)[/tex], Table 1 is a match.
### Table 2
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|---------|---------|
| -22 | -5 |
| -2 | 0 |
| 10 | 3 |
For [tex]\( x = -22 \)[/tex]:
[tex]\[
y = -2 + 4(-22) = -2 - 88 = -90
\][/tex]
The value does not match [tex]\( y = -5 \)[/tex].
Since not all values in Table 2 satisfy the equation [tex]\( y = -2 + 4x \)[/tex], Table 2 is not a match.
### Table 3
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|---------|---------|
| -5 | -18 |
| 0 | -2 |
| 3 | 10 |
For [tex]\( x = -5 \)[/tex]:
[tex]\[
y = -2 + 4(-5) = -2 - 20 = -22
\][/tex]
The value does not match [tex]\( y = -18 \)[/tex].
Since not all values in Table 3 satisfy the equation [tex]\( y = -2 + 4x \)[/tex], Table 3 is not a match.
### Table 4
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|---------|---------|
| -18 | -5 |
For [tex]\( x = -18 \)[/tex]:
[tex]\[
y = -2 + 4(-18) = -2 - 72 = -74
\][/tex]
The value does not match [tex]\( y = -5 \)[/tex].
Since the value in Table 4 does not satisfy the equation [tex]\( y = -2 + 4x \)[/tex], Table 4 is not a match.
### Conclusion
The table that can be created using the equation [tex]\( y = -2 + 4x \)[/tex] is:
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|---------|---------|
| -5 | -22 |
| 0 | -2 |
| 3 | 10 |
Thus, Table 1 is the correct table.
