{"id":"cb_question_bank:bb16f6e5-1e8b-4015-ad6a-b8d82252c393","source_id":"cb_question_bank","source_item_id":"bb16f6e5-1e8b-4015-ad6a-b8d82252c393","external_id":"43d2ddd5-a11f-494c-acca-88dc80fde548","ibn":null,"question_id":"2d0e13a6","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Line k is defined by y equals one fourth x plus 1 . Line j is parallel to line k in the xy -plane. What is the slope of j ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Line <math alttext=\"k\"><mi>k</mi>\n</math> is defined by <math alttext=\"y equals one fourth x plus 1\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>4</mn></mrow></mfrac><mi>x</mi><mo>+</mo><mrow><mn>1</mn></mrow></math>. Line <math alttext=\"j\"><mi>j</mi>\n</math> is parallel to line <math alttext=\"k\"><mi>k</mi>\n</math> in the <em>xy</em>-plane. What is the slope of <math alttext=\"j\"><mi>j</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"one fourth\"><mfrac><mn>1</mn><mn>4</mn></mfrac></math>. It's given that line <math alttext=\"k\"><mi>k</mi>\n</math> is defined by <math alttext=\"y equals one fourth x plus 1\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>x</mi><mo>+</mo><mn>1</mn></math>. It's also given that line <math alttext=\"j\"><mi>j</mi>\n</math> is parallel to line <math alttext=\"k\"><mi>k</mi>\n</math> in the <em>xy</em>-plane. A line in the <em>xy</em>-plane represented by an equation in slope-intercept form&nbsp;<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> has a slope of <math alttext=\"m\"><mi>m</mi>\n</math> and a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma b right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced></math>. Therefore, the slope of line <math alttext=\"k\"><mi>k</mi>\n</math> is <math alttext=\"one fourth\"><mfrac><mn>1</mn><mn>4</mn></mfrac></math>. Since parallel lines have equal slopes, the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is <math alttext=\"one fourth\"><mfrac><mn>1</mn><mn>4</mn></mfrac></math>. Note that 1/4 and .25 are examples of ways to enter a correct answer.</p>","correct_answer":[".25","1/4"],"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":[],"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}}