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Question
The graph represents y = 2x -8.



Which ordered pairs represent a point on the line and solutions to the equation? Select all that apply.

Responses
(-2, 3)
(0, -8)
(0, 4)
(2, 4)
(1, -6)
(2, -4)

Answer 1

To determine which ordered pairs represent points on the line defined by the equation \(y = 2x - 8\), we can substitute the \(x\) values from each ordered pair into the equation and see if the corresponding \(y\) value matches.

1. **For the point \((-2, 3)\)**:
- Substitute \(x = -2\):
\[ y = 2(-2) - 8 = -4 - 8 = -12 \]
- \(y \neq 3\), so this point is NOT on the line.

2. **For the point \((0, -8)\)**:
- Substitute \(x = 0\):
\[ y = 2(0) - 8 = 0 - 8 = -8 \]
- \(y = -8\), so this point IS on the line.

3. **For the point \((0, 4)\)**:
- Substitute \(x = 0\):
\[ y = 2(0) - 8 = 0 - 8 = -8 \]
- \(y \neq 4\), so this point is NOT on the line.

4. **For the point \((2, 4)\)**:
- Substitute \(x = 2\):
\[ y = 2(2) - 8 = 4 - 8 = -4 \]
- \(y \neq 4\), so this point is NOT on the line.

5. **For the point \((1, -6)\)**:
- Substitute \(x = 1\):
\[ y = 2(1) - 8 = 2 - 8 = -6 \]
- \(y = -6\), so this point IS on the line.

6. **For the point \((2, -4)\)**:
- Substitute \(x = 2\):
\[ y = 2(2) - 8 = 4 - 8 = -4 \]
- \(y = -4\), so this point IS on the line.

### Summary of the points that are on the line:
- \((0, -8)\)
- \((1, -6)\)
- \((2, -4)\)

So the ordered pairs that represent points on the line \(y = 2x - 8\) are:
- \((0, -8)\)
- \((1, -6)\)
- \((2, -4)\)