Copyright © 2013 Pearson Education, Inc. Section 3.2 Linear Equations in Two Variables
Example Determine whether the given ordered pair is a solution to the given equation. a. y = x + 5, (2, 7) b. 2x + 3y = 18, (3, 4) Solution a. y = x = = 7 True The ordered pair (2, 7) is a solution. Page 169
Example Determine whether the given ordered pair is a solution to the given equation. a. y = x + 5, (2, 7) b. 2x + 3y = 18, (3, 4) Solution b. 2x + 3y = 18 2(3) + 3( 4) = 18 6 12 = 18 6 18 The ordered pair (3, 4) is NOT a solution. Page 169
Example A table can be used to list solutions to an equation. Complete the table for the equation y = 3x – 1. Solution x 33 11 03 y Page 170
Find five solutions to the equation y = 3x + 2. Choose some x values and then compute the corresponding y values and complete the table. If x = -2, y = 3(-2) + 2 = -4. Ordered pair If x = -1, y = 3(-1) + 2 = -1. Ordered pair If x =0, y = 3(0) + 2 = 2. Ordered pair If x =1, y = 3(1) + 2 = 5. Ordered pair If x =2, y = 3(2) + 2 = 8. Ordered pair Graph on next slide. Finding Solutions of an Equation XY(x,y) Page 170 A table that lists a few solutions is helpful when graphing an equation
Plot the five ordered pairs to obtain the graph of y = 3x + 2 Graph of the Equation XY(X,Y) -2-4(-2,-4) (-1,-1) 02(0,2) 15(1,5) 28(2,8)
Example Make a table of values for the equation y = 3x, and then use the table to graph this equation. Solution Start by selecting a few convenient values for x such as –1, 0, 1, and 2. Then complete the table. xy –1– Plot the points and connect the points with a straight line. Page 171
A linear equation in two variables can be written as Ax + By = C, where A, B, and C are fixed numbers (constants) and A and B are not both equal to 0. The graph of a linear equation in two variables is a line. Linear Equation in Two Variables Page 172
Example Graph the linear equation. Solution Because this equation can be written in standard form, it is a linear equation. Choose any three values for x. xy – Plot the points and connect the points with a straight line. Page 173
Example Graph the linear equation. Solution Because this equation can be written in standard form, it is a linear equation. Choose any three values for x. Plot the points and connect the points with a straight line. xy Page 173
Example Graph the linear equation by solving for y first. Solution Solve for y. xy – Page 174
Plot the five ordered pairs to obtain the graph of y = 3x + 1 (2,7) (1,4) (0,1) (-1,-2) (-2,-5) Graph of the Equation XY(x,y) 27(2,7) 14(1,4) 01(0,1) -2(-1,-2) -2-5(-2,-5)
DONE
Tables of Solutions A table can be used to list solutions to an equation. A table that lists a few solutions is helpful when graphing an equation. Page 170
Basic Concepts Equations can have any number of variables. A solution to an equation with one variable is one number that makes the statement true. Page 168
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Example Graph the linear equation by solving for y first. Solution Solve for y. xy – Page 174
Plot the ordered pairs to obtain the graph of y = 2x Graph of the Equation
Plot the ordered pairs to obtain the graph of y = 2x-2 Graph of the Equation
Plot the ordered pairs to obtain the graph of Graph of the Equation
Plot the five ordered pairs to obtain the graph of y = 3x + 2 Graph of the Equation XY(x,y) -2-4(-2,-4) (-1,-1) 02(0,2) 15(1,5) 28(2,8)