Which equation satisfies the data given in the table?
`{:(x,-1,0,1,2),(y,-3,-1,1,3):}`

Options

A. `y=x-2`
B. `y=2x-1`
C. `y=3x-3`
D. `y=x+1`

Answer

To determine which equation satisfies the data given in the table, we will evaluate each proposed equation against the provided (x, y) pairs. The pairs from the table are:

- (x, y) = (-1, -3)
- (x, y) = (0, -1)
- (x, y) = (1, 1)
- (x, y) = (2, 3)

Let’s evaluate the equations one by one.

### Step 1: Evaluate the first equation \( y = x - 2 \)

1. **For \( x = -1 \)**:
\[ y = -1 - 2 = -3 \]
This matches the table.

2. **For \( x = 0 \)**:
\[ y = 0 - 2 = -2 \]
This does not match the table (should be -1).

3. **For \( x = 1 \)**:
\[ y = 1 - 2 = -1 \]
This does not match the table (should be 1).

4. **For \( x = 2 \)**:
\[ y = 2 - 2 = 0 \]
This does not match the table (should be 3).

### Conclusion for the first equation:
The first equation \( y = x - 2 \) does not satisfy all points in the table.

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### Step 2: Evaluate the second equation \( y = 2x - 1 \)

1. **For \( x = -1 \)**:
\[ y = 2(-1) - 1 = -2 - 1 = -3 \]
This matches the table.

2. **For \( x = 0 \)**:
\[ y = 2(0) - 1 = 0 - 1 = -1 \]
This matches the table.

3. **For \( x = 1 \)**:
\[ y = 2(1) - 1 = 2 - 1 = 1 \]
This matches the table.

4. **For \( x = 2 \)**:
\[ y = 2(2) - 1 = 4 - 1 = 3 \]
This matches the table.

### Conclusion for the second equation:
The second equation \( y = 2x - 1 \) satisfies all points in the table.

### Final Answer:
The equation that satisfies the data given in the table is \( y = 2x - 1 \).

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