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:
- \((-1, -1)\)
- \((0, 2)\)
- \((1, 5)\)
- \((3, 9)\)
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:
-
Removing \((-1, -1)\):
- Slopes among remaining pairs: \((0, 2)\), \((1, 5)\), \((3, 9)\) are not consistent as
3and2are different.
- Slopes among remaining pairs: \((0, 2)\), \((1, 5)\), \((3, 9)\) are not consistent as
-
Removing \((0, 2)\):
- Slopes among remaining pairs: \((-1, -1)\), \((1, 5)\), \((3, 9)\) =
3,2are different.
- Slopes among remaining pairs: \((-1, -1)\), \((1, 5)\), \((3, 9)\) =
-
Removing \((1, 5)\):
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((3, 9)\) = Consistent with
3and2.5.
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((3, 9)\) = Consistent with
-
Removing \((3, 9)\):
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((1, 5)\) are consistent with
3.
- Slopes among remaining pairs: \((-1, -1)\), \((0, 2)\), \((1, 5)\) are consistent with
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: \((1, 5)\)