Question

find the function which is parallel to \\(5x - 2y = 10\\).

\\(2x - 5y = 10\\)
\\(2x + 5y = 10\\)
\\(20x - 8y = 60\\)
all of the choices

Explanation:

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<reasoning>

Find the slope of the given line

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} 5x - 2y &= 10 \\ -2y &= -5x + 10 \\ y &= \frac{5}{2}x - 5 \\ m_1 &= \frac{5}{2} \end{aligned}$$

\]

Determine the slope of a parallel line

Using the Parallel and Perpendicular Lines knowledge point
\[
m_2 = m_1 = \frac{5}{2}
\]

Analyze the given options

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} &\text{Option 1: } 2x - 5y = 10 \implies y = \frac{2}{5}x - 2 \implies m = \frac{2}{5} \\ &\text{Option 2: } 2x + 5y = 10 \implies y = -\frac{2}{5}x + 2 \implies m = -\frac{2}{5} \\ &\text{Option 3: } 20x - 8y = 60 \implies -8y = -20x + 60 \implies y = \frac{5}{2}x - \frac{15}{2} \implies m = \frac{5}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2x - 5y = 10\)</mcq-option>
<mcq-option>(B) \(2x + 5y = 10\)</mcq-option>
<mcq-correct>(C) \(20x - 8y = 60\)</mcq-correct>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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Answer:

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<reasoning>

Find the slope of the given line

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} 5x - 2y &= 10 \\ -2y &= -5x + 10 \\ y &= \frac{5}{2}x - 5 \\ m_1 &= \frac{5}{2} \end{aligned}$$

\]

Determine the slope of a parallel line

Using the Parallel and Perpendicular Lines knowledge point
\[
m_2 = m_1 = \frac{5}{2}
\]

Analyze the given options

Using the Slope of a Linear Function knowledge point
\[

$$\begin{aligned} &\text{Option 1: } 2x - 5y = 10 \implies y = \frac{2}{5}x - 2 \implies m = \frac{2}{5} \\ &\text{Option 2: } 2x + 5y = 10 \implies y = -\frac{2}{5}x + 2 \implies m = -\frac{2}{5} \\ &\text{Option 3: } 20x - 8y = 60 \implies -8y = -20x + 60 \implies y = \frac{5}{2}x - \frac{15}{2} \implies m = \frac{5}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2x - 5y = 10\)</mcq-option>
<mcq-option>(B) \(2x + 5y = 10\)</mcq-option>
<mcq-correct>(C) \(20x - 8y = 60\)</mcq-correct>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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