{"id":"cb_question_bank:ab75e4c2-ac21-425b-8dda-ba303ef003a3","source_id":"cb_question_bank","source_item_id":"ab75e4c2-ac21-425b-8dda-ba303ef003a3","external_id":"dcbc1809-77bc-40b1-b74a-cb105d2b0efa","ibn":null,"question_id":"10c448d6","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A line in the xy -plane has a slope of one ninth and passes through the point left parenthesis 0 comma 14 right parenthesis . Which equation represents this line?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A line in the&nbsp;<em>xy</em>-plane has a slope of&nbsp;<math alttext=\"one ninth\"><mfrac><mn>1</mn><mrow><mn>9</mn></mrow></mfrac></math> and passes through the point&nbsp;<math alttext=\"left parenthesis 0 comma 14 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>14</mn></mrow></mrow></mfenced></math>. Which equation represents this line?</p>","rationale_html":"<p>Choice D is correct. The equation of a line in the <em>xy</em>-plane can be written as <math alttext=\"y equals m x plus b\"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where <math alttext=\"m\"><mi>m</mi>\n</math> represents the slope of the line and&nbsp;<math alttext=\"left parenthesis 0 comma b right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced></math> represents the <em>y</em>-intercept of the line. It's given that the slope of the line is <math alttext=\"one ninth\"><mfrac><mn>1</mn><mn>9</mn></mfrac></math>. It follows that&nbsp;<math alttext=\"m equals one ninth\"><mi>m</mi><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></math>. It's also given that the line passes through the point <math alttext=\"left parenthesis 0 comma 14 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>14</mn></mrow></mfenced></math>. It follows that&nbsp;<math alttext=\"b equals 14\"><mi>b</mi><mo>=</mo><mn>14</mn></math>. Substituting <math alttext=\"one ninth\"><mfrac><mn>1</mn><mn>9</mn></mfrac></math> for <math alttext=\"m\"><mi>m</mi>\n</math> and <math alttext=\"14\"><mn>14</mn>\n</math> for <math alttext=\"b\"><mi>b</mi>\n</math> in <math alttext=\"y equals m x plus b\"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math> yields <math alttext=\"y equals one ninth x plus 14\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mi>x</mi><mo>+</mo><mn>14</mn></math>. Thus, the equation <math alttext=\"y equals one ninth x plus 14\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mi>x</mi><mo>+</mo><mn>14</mn></math> represents this line.</p>\n<p>Choice A is incorrect. This equation represents a line with a slope of <math alttext=\"negative one ninth\"><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></math> and a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma negative 14 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>14</mn></mrow></mfenced></math>.</p>\n<p>Choice B is incorrect. This equation represents a line with a slope of <math alttext=\"negative one ninth\"><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></math> and a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma 14 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>14</mn></mrow></mfenced></math>.</p>\n<p>Choice C is incorrect. This equation represents a line with a slope of <math alttext=\"one ninth\"><mfrac><mn>1</mn><mn>9</mn></mfrac></math> and a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma negative 14 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>14</mn></mrow></mfenced></math>.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"y equals negative one ninth x minus 14\"><mi>y</mi><mo>=</mo><mrow><mrow><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></mrow></mrow><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"y equals negative one ninth x plus 14\"><mi>y</mi><mo>=</mo><mrow><mrow><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></mrow></mrow><mi>x</mi><mo>+</mo><mrow><mn>14</mn></mrow></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"y equals one ninth x minus 14\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>9</mn></mrow></mfrac><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"y equals one ninth x plus 14\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>9</mn></mrow></mfrac><mi>x</mi><mo>+</mo><mrow><mn>14</mn></mrow></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}}