[{"data":1,"prerenderedAt":367},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/ecuacion-explicita-de-la-recta:0":3},{"page":4,"book":25,"news":361,"questionSent":19,"questions":362,"formData":363,"attachments":23,"chartData":23,"pending":19,"chartOptions":364,"afspec":19,"aflink":366},{"id":5,"book_id":6,"chapter_id":7,"name":8,"slug":9,"html":10,"priority":11,"created_at":12,"updated_at":13,"created_by":14,"updated_by":18,"draft":19,"markdown":20,"revision_count":21,"template":19,"owned_by":22,"editor":20,"trends":23,"raw_html":10,"tags":24},4025,23,0,"Ecuación explícita de la recta","ecuacion-explicita-de-la-recta","\u003Cp id=\"bkmrk-la-ecuaci%C3%B3n-expl%C3%ADcit\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/7PzwkiOyPOYiyAPo-exemplo-de-funcao-afim-crescente.jpg\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/scaled-1680-/7PzwkiOyPOYiyAPo-exemplo-de-funcao-afim-crescente.jpg\" alt=\"Exemplo_de_função_afim_crescente.jpg\" width=\"359\" height=\"348\">\u003C/a>La \u003Cstrong>ecuación explícita de la recta\u003C/strong> es la ecuación de la recta en la forma \\(y=mx+n\\), donde \\(m\\) y \\(n\\) indican respectivamente la pendiente y el intercepto (valor en el que la recta intercepta o corta el eje OY cuando x=0).\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-la-ecuaci%C3%B3n-\">\u003Cem>Imagen: La ecuación explícita de la recta y=2x+1 muestra que la recta corta al eje Y en el punto y=1, y que la pendiente es 2, ya que por cada unidad de incremneto en x, la variable y se incrementa en dos unidades, por ejemplo al pasar de (x=o, y=1) a (x=1, y=3).\u003C/em>\u003C/p>",15,"2026-02-21T07:44:26.000000Z","2026-03-09T08:59:35.000000Z",{"id":15,"name":16,"slug":17},1,"Admin","admin",{"id":15,"name":16,"slug":17},false,"",2,{"id":15,"name":16,"slug":17},null,[],{"id":6,"name":26,"slug":27,"description":20,"created_at":28,"updated_at":28,"created_by":15,"updated_by":15,"owned_by":15,"default_template_id":23,"pages":29,"index":60,"shelves":354},"Matemática general","matematica-general","2023-05-22T06:25:36.000000Z",[30,35,40,45,50,55],{"id":31,"name":32,"slug":33,"html":34},2676,"Vector (matemáticas)","vector-matematicas","\u003Cp id=\"bkmrk-en-matem%C3%A1ticas%2C-un-v\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/CudGEDE2vxlpMB0z-vector-by-zureks-es.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/scaled-1680-/CudGEDE2vxlpMB0z-vector-by-zureks-es.png\" alt=\"Vector_by_Zureks_es.png\" width=\"279\" height=\"279\">\u003C/a>En matemáticas, un vector es un segmento o porción de recta que posee un módulo o longitud, una dirección y un sentido u orientación.\u003C/p>\r\n\u003Cp id=\"bkmrk-especificaci%C3%B3n-de-un\">\u003Cstrong>Especificación de un vector\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-un-vector-concreto-%5C\">Un vector concreto \\(\\overrightarrow{a}\\) se define a través de sus componentes o coordenadas \\(\\overrightarrow{a}=(a_1,a_2,...,a_n)\\). Cuando el vector tiene solo dos componentes se puede representar fácilmente en el espacio mediante una flecha, como puede verse en la imagen de abajo, donde se representa el vector \\(\\overrightarrow{a}=(2,3)\\)\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/zPBu61g2wHEnBIuX-vector-examples1.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-left\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/scaled-1680-/zPBu61g2wHEnBIuX-vector-examples1.png\" alt=\"Vector_examples(1).png\" width=\"306\" height=\"306\">\u003C/a>\u003C/p>",{"id":36,"name":37,"slug":38,"html":39},2814,"Combinaciones simples","combinaciones-simples","\u003Cp id=\"bkmrk-una-combinaci%C3%B3n-simp\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-03/2l61tM0MoqYwm87n-combinations-without-repetition-5-choose-3.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-03/scaled-1680-/2l61tM0MoqYwm87n-combinations-without-repetition-5-choose-3.png\" alt=\"Combinations_without_repetition__5_choose_3.png\" width=\"255\" height=\"247\">\u003C/a>Una \u003Cstrong>combinación simple o combinación sin repetición\u003C/strong> es un subconjunto de elementos seleccionado de otro conjunto de elementos distintos distinguibles entre sí, distinguiéndose una combinación simple de otras únicamente por los elementos que están incluidos en la combinación, sin tener en cuenta el orden es que estos se seleccionan o presentan. El calificativo de simple se añade para distinguir la combinación simple de la combinación con repetición en la que los elementos seleccionados pueden aparecer repetidos, siempre sin tener en cuenta el orden. Por ejemplo, las combinaciones simples de dos elementos del conjunto formado por los elementos A, B y C, son AB, AC y BC, teniendo en cuenta, como hemos dicho antes, que el orden no se tiene en cuenta; por ejemplo, AB y BA se consideran la misma combinación por el hecho de que contiene los mismos elementos, aunque sus elementos se indiquen en diferente orden. En la imagen de la derecha puedes ver además las combinaciones simples de 3 elementos que se pueden hacer con los números 1, 2, 3, 4 y 5.\u003C/p>\r\n\u003Cp id=\"bkmrk-en-combinatoria%2C-m%C3%A1s\">En combinatoria, más que cada combinación simple en sí, interesa el número y enumeración de combinaciones simples de k elementos distintos que se pueden formar en total de un conjunto de n elementos, que viene expresado por la siguiente fórmula que no es más que un coeficiente binomial, que se desarrolla con los \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/factorial\">factoriales\u003C/a>\u003C/strong> correspondientes: \u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24c%5En_k%3Dc%28n%2Ck%29%3D%7Bn-%5Cc\">$$C^n_k=C(n,k)={n \\choose k}=\\cfrac{n!}{k!(n-k)!}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-tomando-el-ejemplo-a\">Tomando el ejemplo anterior, el número de combinaciones simples de 2 elementos a partir del conjunto formado por las letras A, B y C se calculan de esta forma:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24c%28n3%2Ck%3D2%29%3D%7B3-%5Cchoo\">$$C(n=3,k=2)={3 \\choose 2}=\\cfrac{3!}{2!(3-2)!}=3$$\u003C/p>\r\n\u003Cp id=\"bkmrk-el-resultado-es-3%2C-q\">El resultado es 3, que se corresponde con la lista de combinaciones que hemos enumerado anteriormente: AB, AC y BC. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ad\">\u003Cstrong>Puede interesarte además\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-permutaciones-simple\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/permutaciones-simples\">\u003Cstrong>Permutaciones simples\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/permutaciones-con-repeticion\">\u003Cstrong>Permutaciones con repetición\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/variaciones-simples\">\u003Cstrong>Variaciones simples\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"id":41,"name":42,"slug":43,"html":44},4099,"Fracciones algebraicas","fracciones-algebraicas","\u003Cp id=\"bkmrk-una-fracci%C3%B3n-algebra\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/ZvNyRusr4cfRFk65-fraccion-algebraica.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/scaled-1680-/ZvNyRusr4cfRFk65-fraccion-algebraica.png\" alt=\"fraccion_algebraica.png\">\u003C/a>Una \u003Cstrong>fracción algebraica\u003C/strong> es una fracción en la que tanto el numerador como el denominador son \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/expresion-algebraica\">expresiones algebraicas\u003C/a>\u003C/strong>. \u003C/p>",{"id":46,"name":47,"slug":48,"html":49},4123,"Diagonal principal","diagonal-principal","\u003Cp id=\"bkmrk-en-%C3%A1lgebra-matricial\">En álgebra matricial, la \u003Cstrong>diagonal principal\u003C/strong> es el cojunto de elementos de una matriz cuadrada que va desde la esquina superior izquierda a la esquina inferior derecha.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagonal-secundaria\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagonal-secundaria-antidiagonal\">\u003Cstrong>Diagonal secundaria\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":51,"name":52,"slug":53,"html":54},4012,"Eje de abscisas","eje-de-abscisas","\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/RK7LpEdhcpAG5o6z-plano-cartesiano.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/scaled-1680-/RK7LpEdhcpAG5o6z-plano-cartesiano.png\" alt=\"plano_cartesiano.png\" width=\"237\" height=\"238\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-el-eje-de-ab\">\u003Cem>Imagen: El eje de abscisas es el eje horizontal correspondiente a la variable x en el plano cartesiano.\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-el-eje-de-abscisas-%28\">El \u003Cstrong>eje de abscisas (*eje de abcisas)\u003C/strong> es el eje de horizontal en un sistema de coordenadas cartesianos. Generalmente, representa los valores de la variable independiente o variable x.  Etimológicamente, proviene del latín \u003Cem>abscisus\u003C/em>, \"cortado\".\u003C/p>",{"id":56,"name":57,"slug":58,"html":59},3350,"Trinomio","trinomio","\u003Cp id=\"bkmrk-un-trinomio-es-una-s\">Un\u003Cstrong> trinomio\u003C/strong> es una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/expresion-algebraica\">expresión algebraica\u003C/a>\u003C/strong> resultado de la suma de tres \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/termino-algebraico\">términos algebraicos\u003C/a>\u003C/strong>, cada uno de los cuales es un producto de \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/constante-matematicas\">constantes \u003C/a>\u003C/strong>y variables, elevadas cada una de ellas a una potencia entera no negativa; se trata por tanto de un polinomio de tres términos. \u003C/p>\r\n\u003Cp id=\"bkmrk-ejemplos-de-trinomio\">\u003Cstrong>Ejemplos de trinomios\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-%5C%284x%5E2%2B2x%2B1%5C%29-%28trino\">\r\n\u003Cli class=\"null\">\\(4x^2+2x+1\\) (trinomio de segundo grado)\u003Cbr>\u003C/li>\r\n\u003Cli class=\"null\">4xy+2x+6y\u003C/li>\r\n\u003Cli class=\"null\">2mn+pq+2\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-monomio-binomio\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/monomio\">\u003Cstrong>Monomio\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/binomio-algebra\">\u003Cstrong>Binomio\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"":61},[62,66,70,74,79,84,89,94,96,101,106,111,116,121,126,131,132,137,139,144,147,152,157,162,166,171,176,181,186,191,196,201,206,211,216,221,226,231,236,241,246,251,256,261,266,271,276,281,286,291,296,301,303,308,313,318,323,325,330,335,340,345,347,352],{"id":63,"name":64,"slug":65,"priority":7,"chapter_name":23},3956,"Algoritmo","algoritmo",{"id":67,"name":68,"slug":69,"priority":15,"chapter_name":23},2552,"Anteperiodo de un número","anteperiodo-de-un-numero",{"id":71,"name":72,"slug":73,"priority":21,"chapter_name":23},1798,"Arista","arista",{"id":75,"name":76,"slug":77,"priority":78,"chapter_name":23},829,"Base de cálculo","base-de-calculo",3,{"id":80,"name":81,"slug":82,"priority":83,"chapter_name":23},2069,"Binomio de Newton","binomio-de-newton",4,{"id":85,"name":86,"slug":87,"priority":88,"chapter_name":23},2573,"Clase de conjuntos","clase-de-conjuntos",5,{"id":90,"name":91,"slug":92,"priority":93,"chapter_name":23},2824,"Combinaciones con repetición (multicombinaciones)","combinaciones-con-repeticion-multicombinaciones",6,{"id":36,"name":37,"slug":38,"priority":95,"chapter_name":23},7,{"id":97,"name":98,"slug":99,"priority":100,"chapter_name":23},2764,"Conjunto vacío","conjunto-vacio",8,{"id":102,"name":103,"slug":104,"priority":105,"chapter_name":23},3799,"Constante (matemáticas)","constante-matematicas",9,{"id":107,"name":108,"slug":109,"priority":110,"chapter_name":23},3999,"Convergencia uniforme","convergencia-uniforme",10,{"id":112,"name":113,"slug":114,"priority":115,"chapter_name":23},3081,"Cuerpo conmutativo, campo (álgebra abstracta)","cuerpo-conmutativo-campo-algebra-abstracta",11,{"id":117,"name":118,"slug":119,"priority":120,"chapter_name":23},3200,"Diagonal secundaria (antidiagonal)","diagonal-secundaria-antidiagonal",12,{"id":122,"name":123,"slug":124,"priority":125,"chapter_name":23},2694,"Dimensión inductiva","dimension-inductiva",13,{"id":127,"name":128,"slug":129,"priority":130,"chapter_name":23},3346,"Discriminante (ecuaciones de segundo grado)","discriminante-ecuaciones-de-segundo-grado",14,{"id":5,"name":8,"slug":9,"priority":11,"chapter_name":23},{"id":133,"name":134,"slug":135,"priority":136,"chapter_name":23},3397,"Ecuaciones de primer grado","ecuaciones-de-primer-grado",16,{"id":51,"name":52,"slug":53,"priority":138,"chapter_name":23},17,{"id":140,"name":141,"slug":142,"priority":143,"chapter_name":23},3869,"Expresión algebraica","expresion-algebraica",18,{"id":145,"name":141,"slug":142,"priority":146,"chapter_name":23},2313,19,{"id":148,"name":149,"slug":150,"priority":151,"chapter_name":23},2409,"Factorial","factorial",20,{"id":153,"name":154,"slug":155,"priority":156,"chapter_name":23},3800,"Función constante","funcion-constante",21,{"id":158,"name":159,"slug":160,"priority":161,"chapter_name":23},4024,"Función identidad","funcion-identidad",22,{"id":163,"name":164,"slug":165,"priority":6,"chapter_name":23},4088,"Función lineal","funcion-lineal",{"id":167,"name":168,"slug":169,"priority":170,"chapter_name":23},3293,"Intervalo abierto","intervalo-abierto",24,{"id":172,"name":173,"slug":174,"priority":175,"chapter_name":23},3291,"Intervalo cerrado","intervalo-cerrado",25,{"id":177,"name":178,"slug":179,"priority":180,"chapter_name":23},4059,"Intervalo mixto (intervalo semiabierto, intervalo semicerrado)","intervalo-mixto-intervalo-semiabierto-intervalo-semicerrado",26,{"id":182,"name":183,"slug":184,"priority":185,"chapter_name":23},3943,"Investigación operativa (investigación de operaciones)","investigacion-operativa-investigacion-de-operaciones",27,{"id":187,"name":188,"slug":189,"priority":190,"chapter_name":23},1129,"Línea poligonal","linea-poligonal",28,{"id":192,"name":193,"slug":194,"priority":195,"chapter_name":23},3223,"Líneas convergentes","lineas-convergentes",29,{"id":197,"name":198,"slug":199,"priority":200,"chapter_name":23},3224,"Líneas divergentes","lineas-divergentes",30,{"id":202,"name":203,"slug":204,"priority":205,"chapter_name":23},1034,"Líneas oblicuas (rectas oblicuas)","lineas-oblicuas-rectas-oblicuas",31,{"id":207,"name":208,"slug":209,"priority":210,"chapter_name":23},949,"Líneas paralelas (rectas paralelas)","lineas-paralelas-rectas-paralelas",32,{"id":212,"name":213,"slug":214,"priority":215,"chapter_name":23},2036,"Menores complementarios","menores-complementarios",33,{"id":217,"name":218,"slug":219,"priority":220,"chapter_name":23},2077,"Números redondos","numeros-redondos",34,{"id":222,"name":223,"slug":224,"priority":225,"chapter_name":23},4026,"Orden de una matriz (dimensión de una matriz)","orden-de-una-matriz-dimension-de-una-matriz",35,{"id":227,"name":228,"slug":229,"priority":230,"chapter_name":23},3433,"Perímetro (geometría)","perimetro-geometria",36,{"id":232,"name":233,"slug":234,"priority":235,"chapter_name":23},777,"Periodo de un número","periodo-de-un-numero",37,{"id":237,"name":238,"slug":239,"priority":240,"chapter_name":23},3003,"Permutaciones circulares","permutaciones-circulares",38,{"id":242,"name":243,"slug":244,"priority":245,"chapter_name":23},2816,"Permutaciones con repetición","permutaciones-con-repeticion",39,{"id":247,"name":248,"slug":249,"priority":250,"chapter_name":23},2408,"Permutaciones simples","permutaciones-simples",40,{"id":252,"name":253,"slug":254,"priority":255,"chapter_name":23},2666,"Productorio","productorio",41,{"id":257,"name":258,"slug":259,"priority":260,"chapter_name":23},1773,"Punto medio","punto-medio",42,{"id":262,"name":263,"slug":264,"priority":265,"chapter_name":23},2914,"Puntos de corte (puntos de intersección)","puntos-de-corte-puntos-de-interseccion",43,{"id":267,"name":268,"slug":269,"priority":270,"chapter_name":23},2464,"Recta real","recta-real",44,{"id":272,"name":273,"slug":274,"priority":275,"chapter_name":23},2537,"Recta secante a una curva","recta-secante-a-una-curva",45,{"id":277,"name":278,"slug":279,"priority":280,"chapter_name":23},3021,"Rectas perpendiculares (rectas ortogonales)","rectas-perpendiculares-rectas-ortogonales",46,{"id":282,"name":283,"slug":284,"priority":285,"chapter_name":23},4032,"Sistema homogéneo (álgebra lineal)","sistema-homogeneo-algebra-lineal",47,{"id":287,"name":288,"slug":289,"priority":290,"chapter_name":23},2800,"Subconjunto","subconjunto",48,{"id":292,"name":293,"slug":294,"priority":295,"chapter_name":23},2661,"Sumatorio","sumatorio",49,{"id":297,"name":298,"slug":299,"priority":300,"chapter_name":23},2037,"Término independiente (término constante)","termino-independiente-termino-constante",50,{"id":56,"name":57,"slug":58,"priority":302,"chapter_name":23},51,{"id":304,"name":305,"slug":306,"priority":307,"chapter_name":23},3625,"Valor (matemáticas)","valor-matematicas",52,{"id":309,"name":310,"slug":311,"priority":312,"chapter_name":23},926,"Valores consecutivos (números consecutivos)","valores-consecutivos-numeros-consecutivos",53,{"id":314,"name":315,"slug":316,"priority":317,"chapter_name":23},2821,"Variaciones con repetición","variaciones-con-repeticion",54,{"id":319,"name":320,"slug":321,"priority":322,"chapter_name":23},2815,"Variaciones simples","variaciones-simples",55,{"id":31,"name":32,"slug":33,"priority":324,"chapter_name":23},56,{"id":326,"name":327,"slug":328,"priority":329,"chapter_name":23},3278,"Vector resultante","vector-resultante",57,{"id":331,"name":332,"slug":333,"priority":334,"chapter_name":23},102,"y=f(x)","yfx",58,{"id":336,"name":337,"slug":338,"priority":339,"chapter_name":23},4095,"Binomio (álgebra)","binomio-algebra",59,{"id":341,"name":342,"slug":343,"priority":344,"chapter_name":23},4098,"Monomio","monomio",60,{"id":41,"name":42,"slug":43,"priority":346,"chapter_name":23},61,{"id":348,"name":349,"slug":350,"priority":351,"chapter_name":23},4100,"Término algebraico","termino-algebraico",62,{"id":46,"name":47,"slug":48,"priority":353,"chapter_name":23},63,[355],{"id":21,"name":356,"slug":357,"description":20,"created_by":15,"updated_by":15,"created_at":358,"updated_at":359,"owned_by":15,"pivot":360},"Matemática y estadística","matematica-y-estadistica","2023-05-05T15:10:53.000000Z","2023-05-07T12:03:04.000000Z",{"book_id":6,"bookshelf_id":21},[],[],{"question":20,"name":20,"email":20,"page_id":5},{"responsive":365,"maintainAspectRatio":19},true,"https://www.amazon.es/hz/audible/mlp/mdp/discovery?actionCode=AMSTM1450129210001&tag=ikusmiraorg-21",1774088544399]