1. Objective I will solve a linear equation graphically.

2. Steps for Solving Linear Equations Graphically Step 1: Write the equation in the form of ax + b = 0. Step 2: Write the related function y = ax + b. Step 3: Graph the equation y = ax + b. The solution of ax + b = 0 is the x-intercept of y = ax + b.

3. Using a Graphical Check for a Solution Solve the equation 4x + 2 = 10 algebraically. Check your solution graphically. 4x + 2 = 10Original Equation 4x = 8Subtract 2 from both sides x = 2Divide both sides by 4 Check answer graphically. 4x + 2 = 10Original Equation 4x - 8 = 0Write equation in ax + b = 0 form y = 4x - 8Write function with 2 variables Graph

4. Solving an Equation Graphically Solve 3x + 5 = 8x graphically. Check your solution algebraically. 3x + 5 = 8xOriginal Equation -5x + 5 = 0Write equation in ax + b = 0 form y = -5x + 5Write function with 2 variables x = 1Graph Check - use substitution 3x + 5 = 8xOriginal Equation 3(1) + 5 = 8(1)Substitute 3 + 5 = 8True

5. Guided Practice 1. Solve -x - 3 = 0.5x algebraically.

6. Calculators Use a graphing calculator to approximate the solution of the linear equation 2.65(4x - 9) = -8.85 + 7.6x Use a graphing calculator to find the intersection point of y = 3 and y = 2x -1.

7. Approximating a Real-Life Solution Based on data from 1980 to 1997, a model for number n (in millions) of registered nurses in the United States is n = 0.055t + 1.26, where t is the number of years since 1980. According to this model, in what year will the United States have 2.5 million registered nurses?

8. Approximating a Real-Life Solution n = 0.055t + 1.26Original Equation 2.5 = 0.055t + 1.26Substitute 0 = 0.055t - 1.24Put in ax + b form, subtract 2.5 y = 0.055t - 1.24Write related function Graph

9. Solve by Graphing Both Sides Another way to graph 2.5 = 0.055t + 1.26 is to write and graph a function for each side of the equation. 2.5 = 0.055t + 1.26Original Equation y = 2.5Function for left side of equation y = 0.055t + 1.26Function for right side of equation Graph both functions in the same coordinate plane. Find the t-coordinate of where the two functions intersect. (t = 22.5)

10. Guided Practice 2. The number of college students from 1990 to 2005 in the United States can be represented by the equation n = 0.025t + 2.45, where n is the number of college students (in millions) and t is the number of years since 1990. According to the equation, in what year will the number of college students in the United States surpass 2.95 million?

11. Independent Practice 1.Solve 2x - 5 = 4x algebraically. 2.Solve (5/2)x - 1 = (9/2)x graphically.