what linear inequality is graphed below?

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

Question

what linear inequality is graphed below?

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

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-Intercept Form", "Linear Inequalities", "Graphing Inequalities" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Linear Inequalities", "Graphing Inequalities" ] } ## Find the boundary line y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &\text{The boundary line crosses the } y\text{-axis at } (0, 2).\ &b = 2 \end{aligned} $$ ## Determine the boundary line slope Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &\text{The line passes through } (0, 2) \text{ and } (-4, -5).\ &m = \frac{-5 - 2}{-4 - 0} = \frac{-7}{-4} = \frac{7}{4} \end{aligned} $$ ## Formulate the boundary line equation Using the *Slope-Intercept Form* knowledge point $$ y = \frac{7}{4}x + 2 $$ ## Determine the inequality sign Using the *Linear Inequalities* and *Graphing Inequalities* knowledge points $$ \begin{aligned} &\text{The boundary line is solid, so the inequality uses } \ge \text{ or } \le.\ &\text{The shaded region is above and to the left of the line.}\ &\text{Testing } (-4, 0) \text{ in the region: } 0 \ge \frac{7}{4}(-4) + 2 \implies 0 \ge -5 \quad (\text{True})\ &\text{The inequality is } y \ge \frac{7}{4}x + 2 \end{aligned} $$

(A) $y \ge \frac{7}{4}x + 2$

(B) $y \le \frac{1}{4}x + 2$

(C) $y \ge 2x + 2$

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

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

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QUESTION IMAGE

Question

Explanation:

Find the boundary line y-intercept

Determine the boundary line slope

Formulate the boundary line equation

Determine the inequality sign

Answer: