Question

Natalie made a graph showing these ordered pairs, representing a proportional relationship.

(0.5, 2), (4, 16), (6.5, 26)




Which ordered pair would be on the same line as Natalie’s ordered pairs?

(1 point)
Responses

(12, 36)
(12, 36)

(2, 4)
(2, 4)

(8, 32)
(8, 32)

(3.5, 12)
(3.5, 12)
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Answer 1

To determine which ordered pair is also on the same line representing the proportional relationship shown by the given ordered pairs (0.5, 2), (4, 16), and (6.5, 26), we first need to establish the constant of proportionality.

We can find the constant of proportionality \( k \) using one of the given points. The general formula for a proportional relationship is:

\[ y = kx \]

1. Using the point (0.5, 2):

\[
2 = k(0.5) \\
k = \frac{2}{0.5} = 4
\]

2. Checking the other pairs with \( k = 4 \):
- For the point (4, 16):

\[
16 = 4(4) \\
16 = 16 \quad \text{(True)}
\]

- For the point (6.5, 26):

\[
26 = 4(6.5) \\
26 = 26 \quad \text{(True)}
\]

Now that we established \( k = 4 \), we can use this constant to check the provided ordered pairs.

- **(12, 36)**:

\[
36 = 4(12) \\
36 = 48 \quad \text{(False)}
\]

- **(2, 4)**:

\[
4 = 4(2) \\
4 = 8 \quad \text{(False)}
\]

- **(8, 32)**:

\[
32 = 4(8) \\
32 = 32 \quad \text{(True)}
\]

- **(3.5, 12)**:

\[
12 = 4(3.5) \\
12 = 14 \quad \text{(False)}
\]

Based on the calculations, the ordered pair that would be on the same line as Natalie’s ordered pairs is **(8, 32)**.