1. Chapter 4 – Graphing Linear Equations 4.7 – Solving Linear Equations Using Graphs

2. Today we will be learning how to: –Solve a linear equation graphically –Use a graph to solve real-life problems

3. 4.7 – Solving Linear Equations Using Graphs Instead of checking equations using Algebra (algebraically), we are now going to use the methods we learned to graph equations to check solutions graphically.

4. 4.7 – Solving Linear Equations Using Graphs STEPS FOR SOLVING LINEAR EQUATIONS GRAPHICALLY –Write the equation in the form mx + b = 0. –Write the related function y = mx + b. –Graph the equation y = mx + b. The solution of mx + b = 0 is the x-intercept of y = mx + b.

5. 4.7 – Solving Linear Equations Using Graphs Example 1 –Solve –x – 3 = 0.5x algebraically. Check your solution graphically.

6. 4.7 – Solving Linear Equations Using Graphs Example 2 –Solve graphically. Check your solution algebraically.

7. 4.7 – Solving Linear Equations Using Graphs Example 3 –Solve 2(x – 3) – 5x = 9 graphically.

8. 4.7 – Solving Linear Equations Using Graphs Example 4 –Based on census data from 1987 to 1995, a model for the hourly wage w of people employed in the production of computers and related goods in the United States in w = 0.409t + 10.74, where t is the number of years since 1987. According to this model, in what year will the hourly wage for these workers be approximately $18.10?

9. 4.7 – Solving Linear Equations Using Graphs Example 4 (continued) –Substitute $18.10 for w. –Write the equation in the form ax + b = 0. –Graph the related function.

10. 4.7 – Solving Linear Equations Using Graphs Example 5 –Another way to solve the equation 18.10 = 0.409t + 10.74 is by writing and graphing an equation for each side of the equation. y = 18.10 y = 0.409t _ 10.74

11. 4.7 – Solving Linear Equations Using Graphs HOMEWORK Page 253 #14 – 36 even