Chapter 4 – Graphing Linear Equations

4.7 – Solving Linear Equations Using Graphs

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.

xx2

91

2

5

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 + 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?

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

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

4.7 – Solving Linear Equations Using Graphs

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