this graph shows the solution to which inequality?

a. \$y < \frac{1}{3}x - 2\$
b. \$y > \frac{1}{3}x - 2\$
c. \$y \le \frac{1}{3}x - 2\$
d. \$y \ge \frac{1}{3}x - 2\$

Question

this graph shows the solution to which inequality?

a. $y < \frac{1}{3}x - 2$
b. $y > \frac{1}{3}x - 2$
c. $y \le \frac{1}{3}x - 2$
d. $y \ge \frac{1}{3}x - 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Shading Half-Planes" ], "new_concepts": [], "current_concepts": [ "Graphing Inequalities", "Slope-Intercept Form", "Shading Half-Planes", "Evaluating Inequalities" ] } ## Find the boundary line equation Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &m = \frac{-1 - (-3)}{3 - (-3)} = \frac{2}{6} = \frac{1}{3}\ &y - (-1) = \frac{1}{3}(x - 3) \implies y = \frac{1}{3}x - 2 \end{aligned} $$ ## Determine the inequality sign Using the *Shading Half-Planes* knowledge point $$ \begin{aligned} &\text{Boundary line is dashed} \implies < \text{ or } >\ &\text{Test point } (0,0) \text{ is in shaded region} \implies 0 > \frac{1}{3}(0) - 2 \implies y > \frac{1}{3}x - 2 \end{aligned} $$

A. $y < \frac{1}{3}x - 2$

B. $y > \frac{1}{3}x - 2$

C. $y \le \frac{1}{3}x - 2$

D. $y \ge \frac{1}{3}x - 2$

{ "elements": [ { "type": "point", "params": [[-3, -3]], "properties": { "name": "(-3, -3)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[3, -1]], "properties": { "name": "(3, -1)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "(1/3)*x - 2", "latex": "y = \frac{1}{3}x - 2"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "dash": 2 } }, { "type": "inequality", "params": [{"js": "(1/3)*x - 2", "latex": "y > \frac{1}{3}x - 2"}, [0, 2]], "properties": { "inverse": true, "strict": true, "fillColor": "rgba(140, 85, 242, 0.3)" } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Find the boundary line equation

Determine the inequality sign

Answer: