Question

question 31 points 1

compute the slopes for the two given functions and determine whether they are parallel or perpendicular.
(i) \\(y = 5x + 10\\)
and (ii) table function

\\(\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 3 & 13 \\\\ \\hline 4 & 18 \\\\ \\hline 5 & 23 \\\\ \\hline 6 & 28 \\\\ \\hline \\end{array}$$

\\)

• they are perpendicular.
• they are parallel.

Explanation:

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<reasoning>

Find the slope of the first function

\[

$$\begin{aligned} &Y = 5X + 10\\ &m_1 = 5 \end{aligned}$$

\]

Find the slope of the second function

\[

$$\begin{aligned} &(X_1, Y_1) = (3, 13),\quad (X_2, Y_2) = (4, 18)\\ &m_2 = \frac{18 - 13}{4 - 3} = \frac{5}{1} = 5 \end{aligned}$$

\]

Compare the slopes

\[

$$\begin{aligned} &m_1 = m_2 = 5 \implies \text{The lines are parallel.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>They are perpendicular.</mcq-option>
<mcq-correct>They are parallel.</mcq-correct>
</answer>

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Answer:

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<reasoning>

Find the slope of the first function

\[

$$\begin{aligned} &Y = 5X + 10\\ &m_1 = 5 \end{aligned}$$

\]

Find the slope of the second function

\[

$$\begin{aligned} &(X_1, Y_1) = (3, 13),\quad (X_2, Y_2) = (4, 18)\\ &m_2 = \frac{18 - 13}{4 - 3} = \frac{5}{1} = 5 \end{aligned}$$

\]

Compare the slopes

\[

$$\begin{aligned} &m_1 = m_2 = 5 \implies \text{The lines are parallel.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>They are perpendicular.</mcq-option>
<mcq-correct>They are parallel.</mcq-correct>
</answer>

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