Chapter 3 Graphing Linear Equations Section 1 The

Chapter 3 Graphing Linear Equations Section 1 The Rectangular Coordinate System; Equations in Two Variables Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1

Concept Ordered Pairs An ordered pair, , is a pair of values listed in the specific order of x first and y second. The values are often referred to as coordinates. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Concept Ordered Pairs Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Concept Solutions of an Equation in Two Variables An ordered pair is a solution of an equation in two variables if it produces a true equation when its coordinates are substituted for x and y. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Example Solutions of an Equation in Two Variables 1 Is a solution of is a solution. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Concept Rectangular Coordinate Plane The rectangular coordinate plane is made up of two number lines, known as axes. The horizontal axis, or x-axis, is used to show the first value of an ordered pair. The vertical axis, or y-axis, is used to show the second value of an ordered pair. The point where the two axes cross is called the origin, and represents the ordered pair Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Concept Rectangular Coordinate Plane Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Concept The quadrants are numbered using Roman numerals. Note that the signs of the coordinates determine the quadrant in which a point lies. Quadrant II Quadrant I ( , +) (+, +) Quadrant III Quadrant IV ( , ) (+, ) Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept Plotting Ordered Pairs To plot an ordered pair on a rectangular coordinate plane we begin at the origin. The x-coordinate tells us how far to the left or right of the origin to move. The ycoordinate then tells us how far up or down to move from there. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9

Example Plotting Ordered Pairs Plot plane. on a rectangular Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Example Write the coordinates for each point shown. We can get to point A by moving to the right 1 and then up 4. A: (1, 4) A B D C B: ( 3, 2) Left 3, up 2 C: ( 2, 2) Left 2, down 2 E F D: (4, 0) Right 4 E: (0, 2) Down 2 F: (4, 3) Right 4, down 3 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11

Concept Standard Form of a Linear Equation A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are real numbers and A and B are not both 0. This is called the standard form of a linear equation in two variables. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 12

Example 2 Complete the following table of ordered pairs with solutions of the linear equation x + y = 7. x y 4 0 1 Substitute x = 4 into the equation Substitute y = 1 for the (4) + y = 7 second ordered pair. y=3 x– 1=7 (4, 3) is a solution. x=8 (8, 1) is a solution. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 13

Example Substitute x = 0 into the equation (0) + y = 7 x 4 y=7 y 3 (0, 7) is a solution. Plot the points on a rectangular coordinate grid. The points appear to fall on a straight line. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2 8 0 1 7 14

Concept Graphing a Linear Equation by Plotting Points Plot ordered pairs that are solutions and draw the straight line that goes through them. Arbitrarily select three values for x, and find the y-coordinates associated with them to find the ordered pairs to plot. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 15

Example 3 Graphing a Linear Equation by Plotting Points Graph Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 16