which of the lines that appear in the graph would be parallel to a line with a slope of 3 and a $y$-intercept at $(0, 3)$?

line $hj$
line $cd$
line $ab$
line $fg$

Question

which of the lines that appear in the graph would be parallel to a line with a slope of 3 and a $y$-intercept at $(0, 3)$?

line $hj$
line $cd$
line $ab$
line $fg$

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": [ "Parallel Line Slopes" ], "new_concepts": [], "current_concepts": [ "Parallel Line Slopes", "Slope Calculation" ] } ## Identify the target slope Using the *Parallel Line Slopes* knowledge point $$ \begin{aligned} &m_{\text{target}} = 3 \end{aligned} $$ ## Calculate the slope of line HJ Using the *Parallel Line Slopes* knowledge point $$ \begin{aligned} &H = (-1, -4),\quad J = (1, 2)\ &m_{HJ} = \frac{2 - (-4)}{1 - (-1)} = \frac{6}{2} = 3 \end{aligned} $$ ## Calculate the slope of line CD Using the *Parallel Line Slopes* knowledge point $$ \begin{aligned} &C = (-3, 0),\quad D = (3, 2)\ &m_{CD} = \frac{2 - 0}{3 - (-3)} = \frac{2}{6} = \frac{1}{3} \end{aligned} $$ ## Calculate the slope of line AB Using the *Parallel Line Slopes* knowledge point $$ \begin{aligned} &A = (-3, 3),\quad B = (4, 3)\ &m_{AB} = \frac{3 - 3}{4 - (-3)} = 0 \end{aligned} $$ ## Calculate the slope of line FG Using the *Parallel Line Slopes* knowledge point $$ \begin{aligned} &F = (-3, -1),\quad G = (3, -3)\ &m_{FG} = \frac{-3 - (-1)}{3 - (-3)} = \frac{-2}{6} = -\frac{1}{3} \end{aligned} $$

line HJ

line CD

line AB

line FG

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

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QUESTION IMAGE

Question

Explanation:

Identify the target slope

Calculate the slope of line HJ

Calculate the slope of line CD

Calculate the slope of line AB

Calculate the slope of line FG

Answer: