a line has a slope of (-\frac{3}{5}). which ordered pairs could be points on a parallel line? select two options.

(square) ((-8, 8)) and ((2, 2))
(square) ((-5, -1)) and ((0, 2))
(square) ((-3, 6)) and ((6, -9))
(square) ((-2, 1)) and ((3, -2))
(square) ((0, 2)) and ((5, 5))

Question

a line has a slope of (-\frac{3}{5}). which ordered pairs could be points on a parallel line? select two options.

(square) ((-8, 8)) and ((2, 2))
(square) ((-5, -1)) and ((0, 2))
(square) ((-3, 6)) and ((6, -9))
(square) ((-2, 1)) and ((3, -2))
(square) ((0, 2)) and ((5, 5))

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Slope of a Line", "Parallel Line Equations" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Parallel Line Equations" ] } ## Identify the parallel slope condition Using the *Parallel Line Equations* knowledge point $$ m_{\text{parallel}} = m = -\frac{3}{5} $$ ## Calculate slope for the first option Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (-8, 8),\quad (x_2, y_2) = (2, 2)\ &m = \frac{2 - 8}{2 - (-8)} = \frac{-6}{10} = -\frac{3}{5} \end{aligned} $$ ## Calculate slope for the second option Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (-5, -1),\quad (x_2, y_2) = (0, 2)\ &m = \frac{2 - (-1)}{0 - (-5)} = \frac{3}{5} \end{aligned} $$ ## Calculate slope for the third option Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (-3, 6),\quad (x_2, y_2) = (6, -9)\ &m = \frac{-9 - 6}{6 - (-3)} = \frac{-15}{9} = -\frac{5}{3} \end{aligned} $$ ## Calculate slope for the remaining options Using the *Slope of a Line* knowledge point $$ \begin{aligned} &\text{For } (-2, 1) \text{ and } (3, -2):\ &m = \frac{-2 - 1}{3 - (-2)} = \frac{-3}{5} = -\frac{3}{5}\ &\text{For } (0, 2) \text{ and } (5, 5):\ &m = \frac{5 - 2}{5 - 0} = \frac{3}{5} \end{aligned} $$

(A) $(-8, 8)$ and $(2, 2)$

(B) $(-5, -1)$ and $(0, 2)$

(C) $(-3, 6)$ and $(6, -9)$

(D) $(-2, 1)$ and $(3, -2)$

(E) $(0, 2)$ and $(5, 5)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Equations" ] }

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Question

Explanation:

Identify the parallel slope condition

Calculate slope for the first option

Calculate slope for the second option

Calculate slope for the third option

Calculate slope for the remaining options

Answer: