Objective I will solve a linear equation graphically.

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.

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

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 = 8True

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

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

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 , where t is the number of years since According to this model, in what year will the United States have 2.5 million registered nurses?

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

Solve by Graphing Both Sides Another way to graph 2.5 = 0.055t is to write and graph a function for each side of the equation. 2.5 = 0.055t Original Equation y = 2.5Function for left side of equation y = 0.055t Function 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)

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 , where n is the number of college students (in millions) and t is the number of years since According to the equation, in what year will the number of college students in the United States surpass 2.95 million?

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