1. 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:
A / A

2. Solving Algebraically
What we have always done: 2x + 3 = x = x = 5

3. 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)

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

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.

6. 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

7. 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

8. A. x = –4
B. x = –9
C. x = 4
D. x = 9

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

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

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

12. Practice
Practice solving equations using a graph on white boards.

13. Homework
Worksheet – “3-2 Solve by Graphing”