3-2 Solving Linear Equations by Graphing Goals: Use a graph to solve a linear equation. Estimate solutions to a linear equation by graphing. Eligible Content: A1.2.1.2.1 / A1.2.1.2.2

Solving Algebraically What we have always done: 2x + 3 = 13 -3 -3 2x = 10 2 2 x = 5

To Solve Using a Graph Rewrite equation to get = 0 Change the 0 into a y Graph the line using a table. Find the x-intercept (root, zero, solution)

Solving Graphically Turn it into an y = equation and graph it to find x intercept. 2x + 3 = 13 -13 - 13 2x – 10 = 0 y = 2x – 10 Make a table to graph! x = 5

Vocabulary Linear Function – a function for which the graph is a line. Root – the solution to the equation. Also called the x-intercept. Zeros – the solutions to the equation. Also called the x-intercept and the root.

𝟏 𝟑 𝒙+𝟏=𝟎 The x-intercept is the solution. x = -3 is the x-intercept x = -3 is the solution x = -3 is the root x = -3 is the zero

Examples Solve each equation using a graph. Check it algebraically. -x – 3 = 2x -3x + 11 = 2 -2x + 7 = 15 x = 3 x = -1 x = 3 x = -4

A. x = –4 B. x = –9 C. x = 4 D. x = 9

A. x = 4; B. x = –4; C. x = –3; D. x = 3;

Special Problems Solve by graphing: 3x + 1 = 3x + 7 No Solution

Solve 4 – 6x = –6x + 3 by graphing. A. x = –1 B. x = 1 C. x = 1 D. no solution

Practice Practice solving equations using a graph on white boards.

Homework Worksheet – “3-2 Solve by Graphing”