{"id":"cb_question_bank:2c0f84e4-6b0c-457e-a05a-8139db3c6a6c","source_id":"cb_question_bank","source_item_id":"2c0f84e4-6b0c-457e-a05a-8139db3c6a6c","external_id":"cc275a34-d420-4dc2-8b26-a526a2d95c32","ibn":null,"question_id":"24854644","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":"What is the equation of the line that passes through the point left parenthesis 0 comma 5 right parenthesis and is parallel to the graph of y equals 7 x plus 4 in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p>What is the equation of the line that passes through the point <math alttext=\"left parenthesis 0 comma 5 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>5</mn></mrow></mrow></mfenced></math> and is parallel to the graph of <math alttext=\"y equals 7 x plus 4\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n</mrow>\n</math> in the <em>xy</em>-plane?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. The equation of a line in the <em>xy</em>-plane can be written in slope-intercept form <math alttext=\"y equals m x plus b\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mi>m</mi>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math>, where <math alttext=\"m\"><mi>m</mi>\n</math> is the slope of the line and <math alttext=\"left parenthesis 0 comma b right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced></math> is its <em>y</em>-intercept. It’s given that the line passes through the point&nbsp;<math alttext=\"left parenthesis 0 comma 5 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math>. Therefore, <math alttext=\"b equals 5\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>. It’s also given that the line is parallel to the graph of <math alttext=\"y equals 7 x plus 4\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n</mrow>\n</math>, which means the line has the same slope as the graph of <math alttext=\"y equals 7 x plus 4\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n</mrow>\n</math>. The slope of the graph of <math alttext=\"y equals 7 x plus 4\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n</mrow>\n</math> is <math alttext=\"7\"><mn>7</mn>\n</math>. Therefore, <math alttext=\"m equals 7\"><mrow>\n\t<mi>m</mi>\n\t<mo>=</mo>\n\t<mn>7</mn>\n</mrow>\n</math>. Substituting <math alttext=\"7\"><mn>7</mn>\n</math> for <math alttext=\"m\"><mi>m</mi>\n</math> and <math alttext=\"5\"><mn>5</mn>\n</math> for <math alttext=\"b\"><mi>b</mi>\n</math> in the equation <math alttext=\"y equals m x plus b\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mi>m</mi>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math> yields <math alttext=\"y equals 7 x plus 5\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>5</mn>\n\t</mrow>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. The graph of this equation passes through the point <math alttext=\"left parenthesis 0 comma 0 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math>, not&nbsp;<math alttext=\"left parenthesis 0 comma 5 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math>, and has a slope of <math alttext=\"5\"><mn>5</mn>\n</math>, not <math alttext=\"7\"><mn>7</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. The graph of this equation passes through the point&nbsp;<math alttext=\"left parenthesis 0 comma 0 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math>, not&nbsp;<math alttext=\"left parenthesis 0 comma 5 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. The graph of this equation passes through the point&nbsp;<math alttext=\"left parenthesis 0 comma 7 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math>, not&nbsp;<math alttext=\"left parenthesis 0 comma 5 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math>, and has a slope of <math alttext=\"5\"><mn>5</mn>\n</math>, not <math alttext=\"7\"><mn>7</mn>\n</math>.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.815000+00:00","source_updated_at":"2023-08-02T20:25:59.815000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"y equals 5 x\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>5</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"y equals 7 x plus 5\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>5</mn>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"y equals 7 x\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>7</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"y equals 5 x plus 7\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>5</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>7</mn>\n\t</mrow>\n</mrow>\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}}