--- title: Graphing Linear Functions - Step-by-Step with Example description: The graph of a linear function is a straight line. Slope and y-intercept, read from the equation. url: https://astra-ai.co/videos/functions/linear-function/graph-of-a-linear-function/ locale: en type: video-lesson keywords: - graph of a linear function - straight line - slope - y-intercept published: 2026-10-01T10:10:27.115Z updated: 2026-10-04T22:01:22.151Z alternates: bg: https://astra-ai.co/bg/videos/funktsii/lineyna-funktsiya/grafika-na-lineyna-funktsiya/ br: https://astra-ai.co/br/videos/funcoes/capitulo-matematica-036/video-matematica-027/ cs: https://astra-ai.co/cs/videos/funkce/linearni-funkce/graf-linearni-funkce/ da: https://astra-ai.co/da/videos/funktioner/lineaer-funktion/grafen-for-en-line-r-funktion/ de: https://astra-ai.co/de/videos/funktionen/lineare-funktion/graph-einer-linearen-funktion/ el: https://astra-ai.co/el/videos/synartiseis/grammiki-synartisi/graph-of-a-linear-function/ en: https://astra-ai.co/videos/functions/linear-function/graph-of-a-linear-function/ en-IN: https://astra-ai.co/en-IN/videos/functions/chapter-7c551282/graph-of-a-linear-function/ en-PH: https://astra-ai.co/en-PH/videos/functions/chapter-7c551282/lesson-eb6fd73d/ es: https://astra-ai.co/es/videos/funciones/funcion-lineal/grafica-de-una-funcion-lineal-guia-paso-a-paso/ es-AR: https://astra-ai.co/es-AR/videos/funciones/capitulo-30/leccion-27/ es-CL: https://astra-ai.co/es-CL/videos/funciones/capitulo-30/leccion-27/ es-PE: https://astra-ai.co/es-PE/videos/funciones/capitulo-video-7c551282/leccion-de-video-eb6fd73d/ et: https://astra-ai.co/et/videos/funktsioonid/lineaarfunktsioon/graafiku-harjutus/ fi: https://astra-ai.co/fi/videos/funktiot/lineaarinen-funktio/lineaarisen-funktion-kuvaaja/ fr: https://astra-ai.co/fr/videos/fonction-mathematique/fonction-lineaire/graphique-dune-fonction-lineaire/ hr: https://astra-ai.co/hr/videos/funkcije/linearna-funkcija/graf-linearne-funkcije/ hu: https://astra-ai.co/hu/videos/fuggvenyek/linearis-fuggveny/linearis-fuggveny-grafikonja/ id: https://astra-ai.co/id/videos/fungsi/fungsi-linear/grafik-fungsi-linear/ it: https://astra-ai.co/it/videos/funzioni/funzione-lineare/grafico-di-una-funzione-lineare/ ja: https://astra-ai.co/ja/videos/functions-ja/30/027/ km: https://astra-ai.co/km/videos/functions/chapter-7c551282/lesson-eb6fd73d/ ko: https://astra-ai.co/ko/videos/functions-ko/30/027/ lo: https://astra-ai.co/lo/videos/lo-a529886c/lo-7c551282/eb6fd73d/ lt: https://astra-ai.co/lt/videos/funkcijos/tiesine-funkcija/pamoka-eb6fd73d/ lv: https://astra-ai.co/lv/videos/funkcijas/lineara-funkcija/stunda-eb6fd73d/ ms: https://astra-ai.co/ms/videos/fungsi/bab-36-matematik-asas/pelajaran-027/ ms-BN: https://astra-ai.co/ms-BN/videos/fungsi/bab-7c551282/pelajaran-eb6fd73d/ mx: https://astra-ai.co/mx/videos/funciones/capitulo-30/leccion-27/ my: https://astra-ai.co/my/videos/my-a529886c/my-7c551282/eb6fd73d/ nl: https://astra-ai.co/nl/videos/functies/lineaire-functie/grafiek-van-een-lineaire-functie/ no: https://astra-ai.co/no/videos/funksjoner/line-r-funksjon/grafen-til-en-line-r-funksjon/ pl: https://astra-ai.co/pl/videos/funkcje/funkcja-liniowa/wykres-funkcji-liniowej/ pt: https://astra-ai.co/pt/videos/funcoes/funcao-linear/grafico-de-uma-funcao-linear/ pt-TL: https://astra-ai.co/pt-TL/videos/funcoes/capitulo-de-video-030/licao-de-video-027/ ro: https://astra-ai.co/ro/videos/functii/functie-liniara/lectie-video-eb6fd73d/ sk: https://astra-ai.co/sk/videos/funkcie/kapitola-030/lekcia-027/ sl: https://astra-ai.co/sl/videos/funkcije/linearna-funkcija/graf-linearne-funkcije/ sr: https://astra-ai.co/sr/videos/funkcije/poglavlje-030/lekcija-027/ sv: https://astra-ai.co/sv/videos/funktioner/linjar-funktion/grafen-for-en-linjar-funktion/ th: https://astra-ai.co/th/videos/fangchan/bot-36-fangchan-ching-sen/botrian-027/ tr: https://astra-ai.co/tr/videos/fonksiyonlar/bolum-030/ders-027/ uk: https://astra-ai.co/uk/videos/uk-topic-19/uk-chapter-36/uk-lesson-eb6fd73d/ vi: https://astra-ai.co/vi/videos/vi-topic-19/vi-chapter-36/do-thi-ham-so-bac-nhat/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-019/shuxue-zhang-036/shuxue-kecheng-027/ zh-TW: https://astra-ai.co/zh-TW/videos/functions/chapter-7c551282/lesson-eb6fd73d/ --- # Graph of a Linear Function > The graph of a linear function is a straight line. This lesson reads the slope and the y-intercept from the equation. ## INTRODUCTION A linear function is one of the basic functions in mathematics and has numerous practical applications. The graphical representation of a linear function is a straight line, which has a characteristic constant slope. ## BASIC PROPERTIES OF A LINEAR FUNCTION A linear function is a function that can be written in the form f(x) = mx + b, where: - 'm' is the slope (gradient) of the line, - 'b' is the y-intercept (the point where the line crosses the y-axis). ### SLOPE OF THE LINE The slope of the line tells us how steep the line is. If 'm' is positive, the line is increasing; if 'm' is negative, it is decreasing. If 'm' = 0, the line is horizontal and represents a constant function. ### Y-INTERCEPT The point 'b' on the y-axis is the point where the line intersects the y-axis. This value tells us where the line is located in the vertical direction. ## EXAMPLE OF DRAWING THE GRAPH OF A LINEAR FUNCTION Let's take the linear function f(x) = 2x + 3 as an example. - **DRAW THE COORDINATE SYSTEM:** First, draw the x-axis and y-axis. - **MARK THE Y-INTERCEPT:** On the y-axis, mark the point (0, 3), since b = 3. - **USE THE SLOPE:** Since m = 2, this means that for every unit we move to the right (positive direction on the x-axis), we move two units up (positive direction on the y-axis). - **PLOT A SECOND POINT:** Choose any value for x, for example, x = 1, and calculate y = 2\*1 + 3 = 5. This gives us a second point (1, 5). - **CONNECT THE POINTS:** Use a ruler to connect the points (0, 3) and (1, 5). The line obtained is the graph of the function f(x) = 2x + 3.