Use the table shown to answer the question.

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: $(1,5)$