Question

find the function which has lesser rate of change.

\\(3x + y = 9\\)

\\(x - y = 5\\)

Explanation:

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<reasoning>

Find the rate of change of the first function

Using the Slope-Intercept Form and Slope of a Linear Function knowledge points
\[

$$\begin{aligned} 3x + y &= 9 \\ y &= -3x + 9 \\ m_1 &= -3 \end{aligned}$$

\]

Find the rate of change of the second function

Using the Slope-Intercept Form and Slope of a Linear Function knowledge points
\[

$$\begin{aligned} x - y &= 5 \\ -y &= -x + 5 \\ y &= x - 5 \\ m_2 &= 1 \end{aligned}$$

\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[

$$\begin{aligned} -3 &< 1 \\ m_1 &< m_2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(3x + y = 9\)</mcq-correct>
<mcq-option>(B) \(x - y = 5\)</mcq-option>
</answer>

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]
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Answer:

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<reasoning>

Find the rate of change of the first function

Using the Slope-Intercept Form and Slope of a Linear Function knowledge points
\[

$$\begin{aligned} 3x + y &= 9 \\ y &= -3x + 9 \\ m_1 &= -3 \end{aligned}$$

\]

Find the rate of change of the second function

Using the Slope-Intercept Form and Slope of a Linear Function knowledge points
\[

$$\begin{aligned} x - y &= 5 \\ -y &= -x + 5 \\ y &= x - 5 \\ m_2 &= 1 \end{aligned}$$

\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[

$$\begin{aligned} -3 &< 1 \\ m_1 &< m_2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(3x + y = 9\)</mcq-correct>
<mcq-option>(B) \(x - y = 5\)</mcq-option>
</answer>

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