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Name: Date: Page 1 of 1 Using Tables to Determine If a Function Is Linear Linear functions have a constant rate of change. You can determine if a table contains a linear function by calculating rates of change. If the same number is added or subtracted to the dependent variable (the y-values), whenever the independent variable (the x-values) changes by some constant amount, the table contains a linear function. The table below contains a linear function because the y-values decrease by 3 whenever the x-values increase by 1. x: y: 2 8 3 5 4 2 5 -1 6 -4 !!!"#$ !" ! 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 = !!!"#$ !" ! = 7 -7 !! ! 8 -10 = −3 1. Determine if each table represents a linear function. Explain why or why not. Comment on !!!"#$ !" ! between coordinate pairs. !!!"#$ !" ! a. x y 9 -15 6 -11 3 -7 0 -3 -3 1 2 10 4 15 Linear Function (Yes / No) Why? b. x -4 -2 0 y 1 3 6 Linear Function (Yes / No) Why? 2. Use the equation to complete the table. Tell whether the relationship is linear. Explain. ! a. 𝑦 = − ! 𝑥 + 2 x y 0 1 2 3 4 x y 12 8 4 0 -4 Linear Function (Yes / No) Why? b. 𝑦 = 𝑥(3 + 𝑥) Linear Function (Yes / No) Why? Activity 4.2.3 CT Algebra I Model Curriculum Version 3.0