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Chapter 4 – Graphing Linear Equations

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.

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Chapter 4 – Graphing Linear Equations

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

  2. 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

  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

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