Linear proportional relationship Linear non-proportional relationship

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Presentation transcript:

Linear proportional relationship Linear non-proportional relationship Linear Functions is about… Strategic Instruction Model (SIM™) University of Kansas Center for Research on Learning (KUCRL.org) a relationship with a constant rate of change represented by a graph that forms a straight line Linear proportional relationship Linear non-proportional relationship 1. Linear: Makes a straight line 1. Linear: Makes a straight line 2. Formula Constant slope represented as m = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 or m = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑥 or m = (𝑦2 −𝑦1) (𝑥2 −𝑥1) 2. Formula Constant slope represented as m = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 or m = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑥 or m = (𝑦2 −𝑦1) (𝑥2 −𝑥1) 3. Equation Represented by y = kx or y = mx + b, where b = 0 For y = kx and y = mx + b, k = the slope, m 3. Equation Represented by y = mx + b, where b ≠ 0 4. y-intercept Passes through the origin (0,0) meaning the y-intercept, b, is 0 Does not pass through the origin (0,0) meaning the y-intercept, b, is not 0 4. y-intercept Does not pass through the origin (0,0) meaning the y-intercept, b, is not 0

1. Linear: Makes a straight line 1. Linear: Makes a straight line Linear Functions is about… Strategic Instruction Model (SIM™) University of Kansas Center for Research on Learning (KUCRL.org) a relationship with a constant rate of change represented by a graph that forms a straight line Direct Variation NOT a Direct Variation 1. Linear: Makes a straight line 1. Linear: Makes a straight line 2. Formula Constant slope represented as m = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 or m = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑥 or m = (𝑦2 −𝑦1) (𝑥2 −𝑥1) 2. Formula Constant slope represented as m = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 or m = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑥 or m = (𝑦2 −𝑦1) (𝑥2 −𝑥1) 3. Equation Represented by y = kx or y = mx + b, where b = 0 For y = kx and y = mx + b, k = the slope, m 3. Equation Represented by y = mx + b, where b ≠ 0 4. y-intercept Passes through the origin (0,0) meaning the y-intercept, b, is 0 Does not pass through the origin (0,0) meaning the y-intercept, b, is not 0 4. y-intercept Does not pass through the origin (0,0) meaning the y-intercept, b, is not 0