which line has a slope of -4?

line b
line c
line e
line d

Question

which line has a slope of -4?

line b
line c
line e
line d

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 Formula", "Linear Graphs" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Linear Graphs" ] } ## Identify the target slope The question asks which line has a slope of $-4$. A slope of $-4$ means that for every $1$ unit the line moves to the right, it goes down by $4$ units. ## Analyze Line B Using the **Slope Formula** and **Linear Graphs** knowledge points: Using the *Slope Formula* and *Linear Graphs* knowledge points $$ \begin{aligned} &\text{Point 1: } (-13, 4)\ &\text{Point 2: } (-12, 0)\ &m = \frac{0 - 4}{-12 - (-13)} = \frac{-4}{1} = -4 \end{aligned} $$ ## Analyze other lines for verification Using the *Slope Formula* and *Linear Graphs* knowledge points $$ \begin{aligned} &\text{Line A (horizontal): } m = 0\ &\text{Line C (vertical): } m = \text{undefined}\ &\text{Line D (increasing): } m = \frac{4 - (-4)}{6 - (-2)} = \frac{8}{8} = 1\ &\text{Line E (decreasing): } m = \frac{-4 - 0}{0 - (-8)} = \frac{-4}{8} = -\frac{1}{2} \end{aligned} $$ ## Match with multiple-choice options The line with a slope of $-4$ is Line B. This corresponds to the first option in the list.

Line B

Line C

Line E

Line D

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the target slope

Analyze Line B

Analyze other lines for verification

Match with multiple-choice options

Answer: