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

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Presentation transcript:

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 § 3.4 The Slope- Intercept Form of a Linear Equation

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-4 Understand Translations of Graphs y = 2x + 3 y = 2x y = 2x – 3 The lines of the graphs of these lines are parallel. We say that the graphs of these equations are vertical translations.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-5 Find the Slope of a Line The slope of a line, m, is the ratio of the vertical change, or rise, to the horizontal change, or run, between any two selected points on the line. Consider the points (1,2) and (3, 6)

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-6 (3, 6) and (1,2) This means the graph is moving up 4 and to the right 2. Horizontal Change Vertical Change Find the Slope of a Line

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-7 Horizontal Change Vertical Change m = 2 Simplifying,, so m = 2 Find the Slope of the Line

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-8 Find the Slope of the Line Slope of a Line Through the Points (x 1, y 1 ) and (x 2, y 2 ) Example Find the slope of the line with points (-2, 3) and (1, -4).

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-9 Positive & Negative Slopes x y x y Positive SlopeNegative Slope Line rises from left to rightLine falls from left to right

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-10 Horizontal Lines Every horizontal line has a slope of 0. y = 2

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-11 Vertical Lines The slope of any vertical line is undefined. x = -4

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-12 Slope-Intercept Form In the slope-intercept form, the graph of a linear equation will always be a straight line in the form y = mx + b were m is the slope of the line and b is the y-intercept (0, b). y = mx + b slopey-intercept Examples: y = 3x – 6 slope is 3 y-intercept is (0, -6) slope is 1/2 y-intercept is (0, 3/2 )

13 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-13 Slope-Intercept Form Example Write the equation -5x + 2y = 8 in slope- intercept form. The slope is 5/2; the y- intercept is (0, 4).