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Which table can be created using the equation below?

[tex]\[ -2 + 4x = y \][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-5 & -22 \\
\hline
0 & -2 \\
\hline
3 & 10 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-22 & -5 \\
\hline
-2 & 0 \\
\hline
10 & 3 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-5 & -18 \\
\hline
0 & -2 \\
\hline
3 & 10 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-18 & -5 \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
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.
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