Question

Use the table shown to answer the question.







Which ordered pair can be removed so that the remaining ordered pairs are part of the same linear function?

(−1, −1)

(0, 2)

(1, 5)

(3, 9)

Answer 1

To determine which ordered pair can be removed so that the remaining ordered pairs represent a linear function, we need to check if the remaining points have a constant slope.

Let's analyze the given points:

1. \((-1, -1)\)
2. \((0, 2)\)
3. \((1, 5)\)
4. \((3, 9)\)

We'll calculate the slope between each pair of points.

**Calculating slopes between pairs:**

- Slope between \((0, 2)\) and \((1, 5)\):
\[
\text{slope} = \frac{5 - 2}{1 - 0} = \frac{3}{1} = 3
\]

- Slope between \((1, 5)\) and \((3, 9)\):
\[
\text{slope} = \frac{9 - 5}{3 - 1} = \frac{4}{2} = 2
\]

- Slope between \((0, 2)\) and \((3, 9)\):
\[
\text{slope} = \frac{9 - 2}{3 - 0} = \frac{7}{3}
\]

- Slope between \((-1, -1)\) and \((0, 2)\):
\[
\text{slope} = \frac{2 - (-1)}{0 - (-1)} = \frac{3}{1} = 3
\]

- Slope between \((-1, -1)\) and \((1, 5)\):
\[
\text{slope} = \frac{5 - (-1)}{1 - (-1)} = \frac{6}{2} = 3
\]

- Slope between \((-1, -1)\) and \((3, 9)\):
\[
\text{slope} = \frac{9 - (-1)}{3 - (-1)} = \frac{10}{4} = 2.5
\]

**Analyzing the slopes:**

From our calculations:

1. Removing \((-1, -1)\):
- Slopes among remaining pairs: \((0, 2)\), \((1, 5)\), \((3, 9)\) are not consistent as `3` and `2` are different.

2. Removing \((0, 2)\):
- Slopes among remaining pairs: \((-1, -1)\), \((1, 5)\), \((3, 9)\) = `3`, `2` are different.

3. Removing \((1, 5)\):
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((3, 9)\) = Consistent with `3` and `2.5`.

4. Removing \((3, 9)\):
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((1, 5)\) are consistent with `3`.

**Conclusion**:
Removing the ordered pair \((1, 5)\) allows the remaining pairs \((-1, -1)\), \((0, 2)\), \((3, 9)\) to be part of the same linear function.

Thus, the correct answer is:
\((1, 5)\)