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Module 4 Lesson 7 What values of x and y make this equation true? y 2x 7 There are infinitely many solutions! Definition of Linear Equation A linear equation is an equation which has: one or two variables the variables appear in separate terms each variable occurs only to the first power line The graph of a linear equation is always a _______. Which of these are linear equations? Why or why not? y=x+1 35 = xy y=–5 3p + 5q = 16 s = 0.2t y = x2 + 7 Steps to Graph a Linear Equation Choose at least three x-values and make a table of values. 2. List the solutions as ordered pairs. 1 3. Graph the ordered pairs. y x 3 2 4. Draw a line through them. 1. x -2 0 2 4 y=½x–3 y Try this x -1 0 1 2 y=x+4 y=x+4 y Try this x -1 0 1 2 y = –2x + 3 y = –2x + 3 y Try this x -1 0 1 2 y = –5 y = –5 y Day 2 : Review Table of Values and Graphing Real-World Example You are filling up your hot tub with water. It is currently at 4 gallons and fills at 5 gallons a minute. Write and graph an equation using the variables: g: total gallons of water m: time (in minutes) 0 2 4 6 g 2 46 m gallons g = 5m + 4 1 2 3 4 5 6 time (minutes) 7 8 Complete a table of values and graph y = 3x – 2 x y x–y=6 x y Complete a table of values and graph y=3 x y x = –7 x y