Question

find the table of values which has greater rate of change.

Explanation:

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<reasoning>

Calculate rate of change for the first table

Using the Rate of Change Comparison knowledge point
\[
m_1 = \frac{19 - 10}{6 - 3} = \frac{9}{3} = 3
\]
\[
m_1 = \frac{25 - 19}{8 - 6} = \frac{6}{2} = 3
\]

Calculate rate of change for the second table

Using the Rate of Change Comparison knowledge point
\[
m_2 = \frac{16 - 11}{3 - 2} = \frac{5}{1} = 5
\]
\[
m_2 = \frac{21 - 16}{4 - 3} = \frac{5}{1} = 5
\]

Calculate rate of change for the third table

Using the Rate of Change Comparison knowledge point
\[
m_3 = \frac{10 - 8}{4 - 3} = \frac{2}{1} = 2
\]
\[
m_3 = \frac{18 - 10}{8 - 4} = \frac{8}{4} = 2
\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[
5 > 3 > 2 \implies m_2 > m_1 > m_3
\]
</reasoning>

<answer>
<mcq-option>(A) Table 1: x = [3, 6, 8], y = [10, 19, 25]</mcq-option>
<mcq-correct>(B) Table 2: x = [2, 3, 4], y = [11, 16, 21]</mcq-correct>
<mcq-option>(C) Table 3: x = [3, 4, 8], y = [8, 10, 18]</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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Answer:

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<reasoning>

Calculate rate of change for the first table

Using the Rate of Change Comparison knowledge point
\[
m_1 = \frac{19 - 10}{6 - 3} = \frac{9}{3} = 3
\]
\[
m_1 = \frac{25 - 19}{8 - 6} = \frac{6}{2} = 3
\]

Calculate rate of change for the second table

Using the Rate of Change Comparison knowledge point
\[
m_2 = \frac{16 - 11}{3 - 2} = \frac{5}{1} = 5
\]
\[
m_2 = \frac{21 - 16}{4 - 3} = \frac{5}{1} = 5
\]

Calculate rate of change for the third table

Using the Rate of Change Comparison knowledge point
\[
m_3 = \frac{10 - 8}{4 - 3} = \frac{2}{1} = 2
\]
\[
m_3 = \frac{18 - 10}{8 - 4} = \frac{8}{4} = 2
\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[
5 > 3 > 2 \implies m_2 > m_1 > m_3
\]
</reasoning>

<answer>
<mcq-option>(A) Table 1: x = [3, 6, 8], y = [10, 19, 25]</mcq-option>
<mcq-correct>(B) Table 2: x = [2, 3, 4], y = [11, 16, 21]</mcq-correct>
<mcq-option>(C) Table 3: x = [3, 4, 8], y = [8, 10, 18]</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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