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

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

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.

4.7 – 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.

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

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

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

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 , where t is the number of years since According to this model, in what year will the hourly wage for these workers be approximately $18.10?

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.

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

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