Solving Linear Equations by Graphing Section 3.2 Solving Linear Equations by Graphing

Linear equations have at most root: a ________; any value that makes the equation _____. solution true Linear equations have at most _____ ______. one root Linear Equation Related Function 3x – 6 = 0 y = 3x – 6 f(x) = 3x – 6

Solve 3x – 6 = 0 (Algebraically): +6 +6 3x = 6 3 3 x = 2 solution ____ is the __________ of 3x – 6 = 0 2

Solve 3x – 6 = 0 (Graphically): Graph y = 3x – 6 x y = 3x – 6 (x, y) (–1, –9) 1 3(–1) – 6 = –3 – 6 = –9 (0, –6) x-intercept 3(0) – 6 = 0 – 6 = –6 (1, –3) 1 3(1) – 6 = 3 – 6 = –3 2 x-intercept __ is the ___________ of y = 3x – 6 2 __ is the ___________ of f(x) = 3x – 6 root

Solve ½ x + 3 = 0 (Algebraically): Clear the denominator. 2(½ x) + 2(3) = 2(0) x + 6 = 0 –6 –6 x = –6 ____ is the __________ of 3x – 6 = 0 –6 solution

Solve ½ x + 3 = 0 (Graphically): Graph y = ½ x + 3 x y = ½ x + 3 (x, y) (–2, 2) 2 ½(–2) + 3 = –1 + 3 = 2 (0, 3) x-intercept ½(0) + 3 = 0 + 3 = 3 (2, 4) 2 ½(2) + 3 = 1 + 3 = 4 -6 x-intercept __ is the ___________ of y = ½ x + 3 -6 __ is the ___________ of f(x) = ½ x + 3 root