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.

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.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Slope of a Linear Function", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Slope of a Linear Function", "Parallel and Perpendicular Lines" ] } ## 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 $$ \begin{aligned} &m_1 = m_2 = 5 \implies \text{The lines are parallel.} \end{aligned} $$

They are perpendicular.

They are parallel.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Parallel and Perpendicular Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Find the slope of the first function

Find the slope of the second function

Compare the slopes

Answer: