(Re)Intro to Linear Equations

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Presentation transcript:

(Re)Intro to Linear Equations Students will be able to identify all major components of a linear equation as well as be able to graph them.

(Re)Intro to Linear Equations 𝑦=𝒎𝑥+𝒃

(Re)Intro to Linear Equations 𝐶𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 𝑎𝑟𝑒 𝑎𝑙𝑤𝑎𝑦𝑠 (𝑥,𝑦)

(Re)Intro to Linear Equations 𝐶𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 𝑎𝑟𝑒 𝑎𝑙𝑤𝑎𝑦𝑠 (𝑥,𝑦)

(Re)Intro to Linear Equations 𝑇ℎ𝑒 𝑂𝑟𝑖𝑔𝑖𝑛 Origin means “the beginning”

(Re)Intro to Linear Equations 𝑆𝑙𝑜𝑝𝑒 𝑠𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 𝑥

(Re)Intro to Linear Equations 𝑆𝑙𝑜𝑝𝑒 𝑠𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 𝑥

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 𝑣. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 (Re)Intro to Linear Equations 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 𝑣. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 𝑣. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 (Re)Intro to Linear Equations 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 𝑣. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑠𝑙𝑜𝑝𝑒

(Re)Intro to Linear Equations 𝑇ℎ𝑒𝑛 𝑤ℎ𝑎𝑡 𝑎𝑏𝑜𝑢𝑡 𝑡ℎ𝑒𝑠𝑒?

𝑅𝑒−𝑊𝑟𝑖𝑡𝑒 𝑡ℎ𝑒 𝑆𝑙𝑜𝑝𝑒 𝐶ℎ𝑎𝑖𝑛 (Re)Intro to Linear Equations 𝑅𝑒−𝑊𝑟𝑖𝑡𝑒 𝑡ℎ𝑒 𝑆𝑙𝑜𝑝𝑒 𝐶ℎ𝑎𝑖𝑛

𝑅𝑒−𝑊𝑟𝑖𝑡𝑒 𝑡ℎ𝑒 𝑆𝑙𝑜𝑝𝑒 𝐶ℎ𝑎𝑖𝑛 (Re)Intro to Linear Equations 𝑅𝑒−𝑊𝑟𝑖𝑡𝑒 𝑡ℎ𝑒 𝑆𝑙𝑜𝑝𝑒 𝐶ℎ𝑎𝑖𝑛 𝑠𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 𝑥

(Re)Intro to Linear Equations 𝑊ℎ𝑎𝑡 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡?

(Re)Intro to Linear Equations 𝑊ℎ𝑎𝑡 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡? 𝑦=𝑚𝑥+𝐛

(Re)Intro to Linear Equations 𝐶𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝐷𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑦 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 →𝑥 𝑖𝑠 𝑧𝑒𝑟𝑜 →(0,𝑏) So what about an x-intercept?

(Re)Intro to Linear Equations 𝐶𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝐷𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑦 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 →𝑥 𝑖𝑠 𝑧𝑒𝑟𝑜 →(0,𝑏) 𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 →𝑦 𝑖𝑠 𝑧𝑒𝑟𝑜 →(𝑥,0)

𝐴𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 𝑡𝑤𝑜 𝑡ℎ𝑖𝑛𝑔𝑠 (Re)Intro to Linear Equations 𝐴𝑛 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 𝑡𝑤𝑜 𝑡ℎ𝑖𝑛𝑔𝑠 An intercept And A point

(Re)Intro to Linear Equations You will always have four things to account for in every linear equation: 𝑦= 𝑥= 𝑚= 𝑏=

(Re)Intro to Linear Equations 𝑦= 𝑥= 𝑚= 𝑏= Write the equation of a line with the point (2,-5) and the y-intercept of 6

Write the equation with slope 4 and coordinate (0,9) (Re)Intro to Linear Equations 𝑦= 𝑥= 𝑚= 𝑏= Write the equation with slope 4 and coordinate (0,9)

Parallel lines have the same slope (Re)Intro to Linear Equations Parallel lines have the same slope

Perpendicular lines have a slope identity of -1 (Re)Intro to Linear Equations Perpendicular lines have a slope identity of -1