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 Slope of a line 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 Slope of a line https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/e/slope-from-two-points 2025-12-28T12:11:43.202987517Z 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/slope-from-table 2022-09-10T01:04:29.754011735Z Calculating slope from tables Practice calculating the slope of a line given some points on the line shown in a table. video https://cdn.kastatic.org/googleusercontent/1fEJmszxEqtPkylSz-ErDUUlRKKPNVZLzDh1joLIWtcdyReCVp8GKOvqIBIO1D5opZsBpEdn15oWgdtHgBBakvAO Calculating slope from tables Practice calculating the slope of a line given some points on the line shown in a table. https://cdn.kastatic.org/ka-youtube-converted/pGsicLglzY8.mp4/pGsicLglzY8.mp4 159 Slope of a line https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/e/slope-table 2025-03-01T15:52:37.13987578Z Slope in a table Practice finding the slope for a linear relationship in a table of values. Jeff Dodds 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 Slope of a line 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 Slope of a line 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 https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines/v/classify-lines 2022-09-10T02:03:40.164764806Z Parallel & perpendicular lines from graph The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. This is a worked example of determining whether given lines are parallel or perpendicular. video https://cdn.kastatic.org/ka_thumbnails_cache/ccf3cc05-28e0-459b-b6d1-521eaf05413c_1280_720_base.png Parallel & perpendicular lines from graph The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. This is a worked example of determining whether given lines are parallel or perpendicular. https://cdn.kastatic.org/ka-youtube-converted/6riBTnlI4fw.mp4/6riBTnlI4fw.mp4 446 Slope of a line https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines/e/classifying-lines-as-parallel--perpendicular--or-neither 2026-03-19T10:07:17.424260476Z Parallel & perpendicular lines from graph Given points that two lines go through or the graph of each line, classify the lines as parallel, perpendicular, or neither. . exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:straight-lines-ncert-new/x0419e5b3b578592a:slope-of-a-line/v/geometric-applications-of-slope-of-a-line 2025-05-22T11:09:14.016569349Z Geometric applications of slope of a line In this video, we discuss some geometric applications of slope of a line. We first prove that three point are collinear. We do this by proving that slope of the line formed by any two points out of three remains the same. We then prove that three points form a right angled triangle. We do this by proving that product of slopes of two of the sides is equal to -1. Finally, we prove that four given points form a parallelogram. We do this by proving that opposite sides have the same slope. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Geometric applications of slope of a line In this video, we discuss some geometric applications of slope of a line. We first prove that three point are collinear. We do this by proving that slope of the line formed by any two points out of three remains the same. We then prove that three points form a right angled triangle. We do this by proving that product of slopes of two of the sides is equal to -1. Finally, we prove that four given points form a parallelogram. We do this by proving that opposite sides have the same slope. https://cdn.kastatic.org/ka-youtube-converted/VAgGvhFtk7Q.mp4/VAgGvhFtk7Q.mp4 588 Slope of a line https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:straight-lines-ncert-new/x0419e5b3b578592a:slope-of-a-line/e/geometric-applications-of-slope-of-a-line 2025-08-08T02:53:40.009522544Z Geometric applications of slope of a line Geometric applications of slope of a line Ashish Gupta exercise