{"id":"cb_question_bank:e9ca836c-d9cb-4ded-8ba3-c26651dd44a5","source_id":"cb_question_bank","source_item_id":"e9ca836c-d9cb-4ded-8ba3-c26651dd44a5","external_id":"f7d44282-a880-4219-88e0-2d034cd8f06b","ibn":null,"question_id":"fb43b85f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A line passes through the points left parenthesis 4 comma 6 right parenthesis and left parenthesis 15 comma 24 right parenthesis in the xy -plane. What is the slope of the line?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A line passes through the points <math alttext=\"left parenthesis 4 comma 6 right parenthesis\"><mfenced><mrow><mrow><mn>4</mn></mrow><mo>,</mo><mrow><mn>6</mn></mrow></mrow></mfenced></math> and <math alttext=\"left parenthesis 15 comma 24 right parenthesis\"><mfenced><mrow><mrow><mn>15</mn></mrow><mo>,</mo><mrow><mn>24</mn></mrow></mrow></mfenced></math> in the <em>xy</em>-plane. What is the slope of the line?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"StartFraction 18 Over 11 EndFraction\"><mfrac>\n\t<mn>18</mn>\n\t<mn>11</mn>\n</mfrac>\n</math>. For a line that passes through the points&nbsp;<math alttext=\"left parenthesis x 1 comma y 1 right parenthesis\"><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><msub><mi>y</mi><mn>1</mn></msub></mrow></mfenced></math> and&nbsp;<math alttext=\"left parenthesis x 2 comma y 2 right parenthesis\"><mfenced><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><msub><mi>y</mi><mn>2</mn></msub></mrow></mfenced></math> in the <em>xy</em>-plane, the slope of the line can be calculated using the slope formula, <math alttext=\"m equals StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction\"><mi>m</mi><mo>=</mo><mfrac><mrow><msub><mi>y</mi><mn>2</mn></msub><mo>-</mo><msub><mi>y</mi><mn>1</mn></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac></math>. It's given that a line passes through the points&nbsp;<math alttext=\"left parenthesis 4 comma 6 right parenthesis\"><mfenced><mrow><mn>4</mn><mo>,</mo><mn>6</mn></mrow></mfenced></math> and&nbsp;<math alttext=\"left parenthesis 15 comma 24 right parenthesis\"><mfenced><mrow><mn>15</mn><mo>,</mo><mn>24</mn></mrow></mfenced></math> in the <em>xy</em>-plane. Substituting <math alttext=\"left parenthesis 4 comma 6 right parenthesis\"><mfenced><mrow><mn>4</mn><mo>,</mo><mn>6</mn></mrow></mfenced></math> for <math alttext=\"left parenthesis x 1 comma y 1 right parenthesis\"><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><msub><mi>y</mi><mn>1</mn></msub></mrow></mfenced></math> and <math alttext=\"left parenthesis 15 comma 24 right parenthesis\"><mfenced><mrow><mn>15</mn><mo>,</mo><mn>24</mn></mrow></mfenced></math> for <math alttext=\"left parenthesis x 2 comma y 2 right parenthesis\"><mfenced><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><msub><mi>y</mi><mn>2</mn></msub></mrow></mfenced></math>&nbsp;in the slope formula, <math alttext=\"m equals StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction\"><mi>m</mi><mo>=</mo><mfrac><mrow><msub><mi>y</mi><mn>2</mn></msub><mo>-</mo><msub><mi>y</mi><mn>1</mn></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac></math>, yields <math alttext=\"m equals StartFraction 24 minus 6 Over 15 minus 4 EndFraction\"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn></mrow><mrow><mn>15</mn><mo>-</mo><mn>4</mn></mrow></mfrac></math>, or <math alttext=\"m equals StartFraction 18 Over 11 EndFraction\"><mi>m</mi><mo>=</mo><mfrac><mn>18</mn><mn>11</mn></mfrac></math>. Therefore, the slope of the line is <math alttext=\"StartFraction 18 Over 11 EndFraction\"><mfrac>\n\t<mn>18</mn>\n\t<mn>11</mn>\n</mfrac>\n</math>. Note that 18/11 and 1.636 are examples of ways to enter a correct answer.</p>","correct_answer":["1.636","18/11"],"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":[],"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}}