https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:linear-equations-in-two-variables/x06d55bfa213a79fd:graph-of-a-linear-equation-in-two-variables/v/graphical-representation-of-y-mx 2026-02-18T21:20:35.275198076Z Graphical representation of y=mx Why does y = mx always pass through the origin? Let's find out! In this video, we start with a fun real-world problem: if a school has 30 girls, how many boys are there? Using this scenario, we build the equation y = 3x and explore the fascinating world of linear equations and their graphs. Watch as we plot coordinate points, draw straight lines, and discover why every equation of the form y = mx must pass through (0, 0). We'll also compare different lines like y = x, y = 2x, and y = -2x to understand how the value of ""m"" affects the steepness (slope) and direction of the line. Whether m is positive or negative changes everything, and we'll show you exactly why! Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Graphical representation of y=mx Why does y = mx always pass through the origin? Let's find out! In this video, we start with a fun real-world problem: if a school has 30 girls, how many boys are there? Using this scenario, we build the equation y = 3x and explore the fascinating world of linear equations and their graphs. Watch as we plot coordinate points, draw straight lines, and discover why every equation of the form y = mx must pass through (0, 0). We'll also compare different lines like y = x, y = 2x, and y = -2x to understand how the value of ""m"" affects the steepness (slope) and direction of the line. Whether m is positive or negative changes everything, and we'll show you exactly why! 405 Visualising Linear Relationships https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:linear-equations-in-two-variables/x06d55bfa213a79fd:graph-of-a-linear-equation-in-two-variables/e/graphical-representation-of-an-equation-of-the-form-y-mx 2026-04-08T00:54:09.631945657Z Graphical representation of an equation of the form y = mx In this exercise students learn to the concepts related to plotting the lines of the form y=mx Devashish Phadnis exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:standard-form/v/plotting-x-y-relationships 2022-11-16T04:22:43.7414897Z Graphing a linear equation: 5x+2y=20 We can graph a the linear equation like 5x + 2y = 20 by rewriting it so y is isolated, then plugging in x values to find their corresponding y-values in a table. We can then graph those x-y pairs as points on a graph. Sal Khan video https://cdn.kastatic.org/googleusercontent/7yJGdQjBdDMseTIPkIpXZxn7GUpJn5TMzpUIYAKsNY0TpBXBHGhtX0u1feQq-pW_wqs1jIv0scQ26dpCPReFDMiX1g Graphing a linear equation: 5x+2y=20 We can graph a the linear equation like 5x + 2y = 20 by rewriting it so y is isolated, then plugging in x values to find their corresponding y-values in a table. We can then graph those x-y pairs as points on a graph. https://cdn.kastatic.org/ka-youtube-converted/86NwKBcOlow.mp4/86NwKBcOlow.mp4 269 Visualising Linear Relationships https://www.khanacademy.org/math/math-1-illustrative-math-aligned/x193529144fa1e1f6:linear-equations-and-systems/x193529144fa1e1f6:equations-and-their-graphs-optional/v/graphs-of-linear-equations 2020-08-25T18:06:02Z Graphing a linear equation: y=2x+7 Learn how to create a graph of the linear equation y = 2x + 7. Sal Khan video https://cdn.kastatic.org/googleusercontent/XYwg1vPlZG5HWWPhZNvx7nQdglN2JFhr87LLpQlDMpTvK3YSQoP73Gzlz_msZgZx0v6tgReECIYcGCU26QU103QO Graphing a linear equation: y=2x+7 Learn how to create a graph of the linear equation y = 2x + 7. https://cdn.kastatic.org/ka-youtube-converted/rgvysb9emcQ.mp4/rgvysb9emcQ.mp4 790 Visualising Linear Relationships https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:standard-form/e/graph-from-standard-form-equation 2026-04-07T22:23:57.656416987Z Graph from linear standard form Find the graph of a linear equation given in standard form. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/introduction-to-slope 2023-09-29T20:10:37.268517027Z Intro to slope Slope tells us how steep a line is. It's like measuring how quickly a hill goes up or down. We find the slope by seeing how much we go up or down (vertical change) for each step to the right (horizontal change). If a line goes up 2 steps for every 1 step to the right, its slope is 2. video https://cdn.kastatic.org/googleusercontent/s1jE8xrZxjyUjYW3PI9BB1Mxz4E7equCqGbkEukkpuVrWYXLUscHO_DmhTAhux9EjAYmTOCAJx8fqDbDaAbwlEg Intro to slope Slope tells us how steep a line is. It's like measuring how quickly a hill goes up or down. We find the slope by seeing how much we go up or down (vertical change) for each step to the right (horizontal change). If a line goes up 2 steps for every 1 step to the right, its slope is 2. https://cdn.kastatic.org/ka-youtube-converted/MeU-KzdCBps.mp4/MeU-KzdCBps.mp4 416 Visualising Linear Relationships https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line-2 2023-09-29T20:10:37.268517027Z Worked example: slope from two points Let's find the slope of the line that goes through the ordered pairs (4,2) and (-3, 16). The slope, or steepness, of a line is found by dividing the vertical change (rise) by the horizontal change (run). The formula is slope =(y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line. Sal Khan video https://cdn.kastatic.org/googleusercontent/PxBg2KX9haoU35DgDnNZNQT3OYNxJjLO0hRF4c5oRQPWs9fw_naaVnJnrS1qav0CtySrupVLoyiOMWJ3uCF_x5I Worked example: slope from two points Let's find the slope of the line that goes through the ordered pairs (4,2) and (-3, 16). The slope, or steepness, of a line is found by dividing the vertical change (rise) by the horizontal change (run). The formula is slope =(y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line. https://cdn.kastatic.org/ka-youtube-converted/WkspBxrzuZo.mp4/WkspBxrzuZo.mp4 432 Visualising Linear Relationships https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/e/slope-from-two-points 2026-05-04T16:10:46.51963925Z Slope from two points Find the slope of the line that goes through the two points that are given to you. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/positive-and-negative-slope 2021-06-21T15:29:05Z Positive & negative slope Sal analyzes what it means for a slope to be positive or negative (spoiler: it affects the direction of the line!) video https://cdn.kastatic.org/googleusercontent/qKzK_1Y1okuQwqlOwe_2PkPDXtA-7qTqPi79AEm6sWSXKMj9g_HbyBcFSxPLiF8BzEiPuctAQkGTL8eBpfnBmbtKcw Positive & negative slope Sal analyzes what it means for a slope to be positive or negative (spoiler: it affects the direction of the line!) https://cdn.kastatic.org/ka-youtube-converted/EQoNfxToez0.mp4/EQoNfxToez0.mp4 302 Visualising Linear Relationships https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line 2021-06-21T15:29:13Z Worked example: slope from graph The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x. Sal Khan video https://cdn.kastatic.org/googleusercontent/yS8TgEKoKA9bxbEUlRnkKhItBgWvaNJP3EYPBzXQc5PrYcbsqMUrwqAfIB67dHCyuH4gKk47tCUqVDGWMVbDtPUH Worked example: slope from graph The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x. https://cdn.kastatic.org/ka-youtube-converted/R948Tsyq4vA.mp4/R948Tsyq4vA.mp4 280 Visualising Linear Relationships https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/e/slope-from-a-graph 2025-02-27T11:46:16.621461116Z Slope from graph Find the slope of a line on the coordinate plane. Tomer Gal exercise