4.5 linear inequalities quiz

which inequality should be graphed with a dashed line?

$y \ge 4x + 7$
$y \ge 3$
$y \le -\frac{3}{2}x + 7$
$y

Question

4.5 linear inequalities quiz

which inequality should be graphed with a dashed line?

$y \ge 4x + 7$
$y \ge 3$
$y \le -\frac{3}{2}x + 7$
$y < \frac{1}{2}x - 4$

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": [ "Linear Inequalities", "Graphing Inequalities" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "Graphing Inequalities" ] } ## Identify the graphing rule for boundary lines Using the **Graphing Inequalities** knowledge point $$ \begin{aligned} &\text{Strict inequalities } (<, >) \implies \text{Dashed boundary line}\ &\text{Non-strict inequalities } (\le, \ge) \implies \text{Solid boundary line} \end{aligned} $$ ## Analyze the given options Using the **Linear Inequalities** knowledge point $$ \begin{aligned} &y \ge 4x + 7 \implies \ge \text{ is non-strict (solid line)}\ &y \ge 3 \implies \ge \text{ is non-strict (solid line)}\ &y \le -\frac{3}{2}x + 7 \implies \le \text{ is non-strict (solid line)}\ &y < \frac{1}{2}x - 4 \implies < \text{ is strict (dashed line)} \end{aligned} $$

(A) $y \ge 4x + 7$

(B) $y \ge 3$

(C) $y \le -\frac{3}{2}x + 7$

(D) $y < \frac{1}{2}x - 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the graphing rule for boundary lines

Analyze the given options

Answer: