1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Graphs 3.2 – Functions 3.3 – Linear Functions: Graphs and Applications 3.4 – The Slope-Intercept Form of a Linear Equation 3.5 – The Point-Slope Form of a Linear Equation 3.6 – The Algebra of Functions 3.7 – Graphing Linear Inequalities Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-3 § 3.1 Graphs

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-4 Definitions A graph shows the relationship between two variables in an equation. The Cartesian (rectangular) coordinate system is a grid system used to draw graphs. It is named after its developer, René Descartes ( ).

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-5 Definitions The two intersecting axis form four quadrants, numbered I through IV. IVIII III The horizontal axis is called the x-axis. The vertical axis is called the y-axis. x y

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-6 Definitions The point of intersection of the two axes is called the origin. Origin, or the value of the x and the value of the y The coordinates, or the value of the x and the value of the y determines the point. This is also called an ordered pair. x y (0, 0)

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-7 Plotting Points Plot the point (3, -4). The x-coordinate is 3 and the y-coordinate is –4. Starting at the origin, move 3 places to the right.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-8 Plotting Points Plot the point (3, -4). The x-coordinate is 3 and the y-coordinate is –4. Then move 4 places down.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-9 Plotting Points Plot the point (3, -4). The x-coordinate is 3 and the y-coordinate is –4. (3, -4)

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-10 Linear Equations A linear equation in two variables is an equation that can be put in the form ax + by = c where a, b, and c are real numbers. This is called the standard form of an equation. Examples: 4x – 3y = 12 x + 2y = -35

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-11 Solutions to Equations The solution to an equation is the ordered pair that can be substituted into the equation without changing the “validity” of the equation. Is (3, 0) a solution to the equation 4x – 3y = 12? 4x – 3y = 12 4(3) – 3(0) = – 0 = = 12 Yes, it is a solution.

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-12 Graphing A graph of an equation is an illustration of the set of points whose ordered pairs are solutions to the equation. A set of points that are in a straight line are collinear. The points (-1, 4), (1, 1) and (4, -3) are collinear.

13 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-13 Graph Nonlinear Equations Equations whose graphs are not straight lines are called nonlinear equations. Example: Graph y = x 2 – 4. Use the following values for x: -3, -2, -1, 0, 1, 2, and 3.