Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 3 Introduction to Graphing

3-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Graphing Linear Equations Solutions of Equations Graphing Linear Equations Applications 3.2

3-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Determine whether each of the following pairs is a solution of 4y + 3x = 18: a) (2, 3); b)(1, 5). Solution a) We substitute 2 for x and 3 for y. 4y + 3x = | | = 18 True Since 18 = 18 is true, the pair (2, 3) is a solution.

3-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example b) We substitute 1 for x and 5 for y. 4y + 3x = | | = 18 False Since 23 = 18 is false, the pair (1, 5) is not a solution.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. To Graph a Linear Equation 1. Select a value for one coordinate and calculate the corresponding value of the other coordinate. Form an ordered pair. This pair is one solution of the equation. 2. Repeat step (1) to find a second ordered pair. A third ordered pair can be used as a check. 3. Plot the ordered pairs and draw a straight line passing through the points. The line represents all solutions of the equation.

3-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Graph: y = –4x + 1 Solution We select convenient values for x and compute y, and form an ordered pair. If x = 2, then y =  4(2) + 1 =  7 and (2,  7) is a solution. If x = 0, then y =  4(0) + 1 = 1 and (0, 1) is a solution. If x =  2, then y =  4(  2) + 1 = 9 and (  2, 9) is a solution.

3-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Results are often listed in a table. (1) Choose x. (2) Compute y. (3) Form the pair (x, y). (4) Plot the points. xy(x, y) 2 77(2,  7) 01(0, 1) 22 9 (  2, 9)

3-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Note that all three points line up. If they didn’t we would know that we had made a mistake. Finally, use a ruler or other straightedge to draw a line. Every point on the line represents a solution of y =  4x + 1

3-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Graph x + 2y = 6 Solution Select some convenient x-values and compute y-values. If x = 6, then 6 + 2y = 6  y = 0 If x = 0, then 0 + 2y = 6  y = 3 If x = 2, then 2 + 2y = 6  y = 2 xy(x, y) 60(6, 0) 03(0, 3) 22(2, 2)

3-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Graph 4y = 3x Solution Begin by solving for y. To graph we can select values of x that are multiples of 4. This will allow us to avoid fractions when corresponding y-values are computed.

3-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Select some convenient x-values and compute y-values. If x = 0, then ¾ (0) = 0 If x = 4, then ¾ (4) = 3 If x =  4, then ¾ (  4) =  3 xy(x, y) 00(0, 0) 43(4, 3) 44 33(  4,  3)

3-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The cost c, in dollars, of shipping a FedEx Priority Overnight package weighing 1 lb or more a distance of 1001 to 1400 mi is given by c = 2.8w where w is the package’s weight in pounds. Graph the equation and then use the graph to estimate the cost of shipping a 10 ½-pound package.

3-13 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Select values for w and then calculate c. c = 2.8w If w = 2, then c = 2.8(2) = If w = 4, then c = 2.8(4) = If w = 8, then c = 2.8(8) = wc

3-14 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Weight (in pounds) Mail cost (in dollars) Plot the points. To estimate an 10 ½ pound package, we locate the point on the line that is above 10 ½ and then find the value on the c-axis that corresponds to that point. The cost of shipping an 10 ½ pound package is about $ ½ pounds