{"id":"cb_question_bank:610781bd-312c-4ee8-b488-02beef6bb456","source_id":"cb_question_bank","source_item_id":"610781bd-312c-4ee8-b488-02beef6bb456","external_id":"4e92e788-6fae-4f7c-a838-84939a7bdd2f","ibn":null,"question_id":"bf5f80c6","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y < − 4 x + 4 Which point ( x , y ) is a solution to the given inequality in the x y -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math><mrow><mi>y</mi><mo>&lt;</mo><mo>−</mo><mrow><mn>4</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>4</mn></mrow></mrow></math></p>\n<p>Which point (<math><mi>x</mi>\n</math>, <math><mi>y</mi>\n</math>) is a solution to the given inequality in the <math><mrow>\n\t<mi>x</mi>\n\t<mi>y</mi>\n</mrow>\n</math>-plane?</p>","rationale_html":"<p>Choice D is correct. For a point&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> to be a solution to the given inequality in the <em>xy</em>-plane, the value of the point’s <em>y</em>-coordinate must be less than the value of&nbsp;<math alttext=\"minus 4 x plus 4\"><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></math>, where <math alttext=\"x\"><mi>x</mi>\n</math> is the value of the <em>x</em>-coordinate of the point. This is true of the point&nbsp;<math alttext=\"left parenthesis negative 4 comma 0 right parenthesis\"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> because&nbsp;<math alttext=\"0 less than minus 4 left parenthesis negative 4 right parenthesis plus 4\"><mn>0</mn><mo>&lt;</mo><mo>-</mo><mn>4</mn><mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mn>4</mn></math>, or&nbsp;<math alttext=\"0 less than 20\"><mn>0</mn><mo>&lt;</mo><mn>20</mn></math>. Therefore, the point&nbsp;<math alttext=\"left parenthesis negative 4 comma 0 right parenthesis\"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math>&nbsp;is a solution to the given inequality.</p>\n<p><br>Choices A, B, and C are incorrect. None of these points are a solution to the given inequality because each point’s <em>y</em>-coordinate is greater than the value of&nbsp;<math alttext=\"minus 4 x plus 4\"><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></math>&nbsp;for the point’s <em>x</em>-coordinate.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"<p>(<math><mn>-4</mn>\n</math>, <math><mn>0</mn>\n</math>)</p>","ord":0},{"label":"B","content_html":"<p>(<math><mn>0</mn>\n</math>, <math><mn>5</mn>\n</math>)</p>","ord":1},{"label":"C","content_html":"<p>(<math><mn>2</mn>\n</math>, <math><mn>1</mn>\n</math>)</p>","ord":2},{"label":"D","content_html":"<p>(<math><mn>2</mn>\n</math>, <math><mn>-1</mn>\n</math>)</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}