Chapter 3 Graphs and Functions Copyright 2015 2011

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

Chapter Sections 3. 1 – 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 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -2 2

§ 3. 4 The Slope. Intercept Form of a Linear Equation Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -

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

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) Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -5 5

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

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

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). Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -8 8

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

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

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

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). slope y-intercept y = mx + b y = 3 x – 6 slope is 3 Examples: y-intercept is (0, -6) slope is 1/2 y-intercept is (0, 3/2 ) Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -12 12

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