Question

compute the slopes for the two given functions and determine which function has a greater rate of change.
(i)table function
(ii)graph function

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 3 & 6 \\\\ \\hline 4 & 8 \\\\ \\hline 5 & 10 \\\\ \\hline 6 & 12 \\\\ \\hline \\end{array}$$

\bigcirc$ the graph function has a greater rate of change.
\bigcirc$ the table function has a greater rate of change.

Explanation:

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<reasoning>

Calculate the slope of the table function

Using the Slope of a Linear Function knowledge point
\[
m_{\text{table}} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 6}{4 - 3} = 2
\]

Calculate the slope of the graph function

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} &(x_1, y_1) = (0, 2)\\ &(x_2, y_2) = (-2, 0)\\ &m_{\text{graph}} = \frac{0 - 2}{-2 - 0} = 1 \end{aligned}$$

\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[

$$\begin{aligned} &m_{\text{table}} = 2\\ &m_{\text{graph}} = 1\\ &2 > 1 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The graph function has a greater rate of change.</mcq-option>
<mcq-correct>The table function has a greater rate of change.</mcq-correct>
</answer>

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Answer:

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<reasoning>

Calculate the slope of the table function

Using the Slope of a Linear Function knowledge point
\[
m_{\text{table}} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 6}{4 - 3} = 2
\]

Calculate the slope of the graph function

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} &(x_1, y_1) = (0, 2)\\ &(x_2, y_2) = (-2, 0)\\ &m_{\text{graph}} = \frac{0 - 2}{-2 - 0} = 1 \end{aligned}$$

\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[

$$\begin{aligned} &m_{\text{table}} = 2\\ &m_{\text{graph}} = 1\\ &2 > 1 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The graph function has a greater rate of change.</mcq-option>
<mcq-correct>The table function has a greater rate of change.</mcq-correct>
</answer>

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