1. Copyright © 2007 Pearson Education, Inc. Slide 1-1

2. Copyright © 2007 Pearson Education, Inc. Slide 1-2 Chapter 1:Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions 1.3 Linear Functions 1.4 Equations of Lines and Linear Models 1.5 Linear Equations and Inequalities 1.6 Applications of Linear Functions

3. Copyright © 2007 Pearson Education, Inc. Slide 1-3 1.1 Real Numbers and the Rectangular Coordinate System Sets of Real Numbers: Natural Numbers: Whole Numbers: Integers: Rational Numbers: Irrational Numbers:

4. Copyright © 2007 Pearson Education, Inc. Slide 1-4 1.1 Example Indicate the set each number belongs to:

5. Copyright © 2007 Pearson Education, Inc. Slide 1-5 1.1 The Set of Real Numbers and the Number Line Real Numbers: Every real number corresponds to a point on the number line. -4 -3 -2 -1 0 1 2 3 4

6. Copyright © 2007 Pearson Education, Inc. Slide 1-6 1.1 The Rectangular Coordinate System The number corresponding to a particular point on the number line is called the coordinate of the point. This correspondence is called a coordinate system.

7. Copyright © 2007 Pearson Education, Inc. Slide 1-7 1.1 The Coordinate Plane Cartesian Coordinate System –xy-plane (or coordinate plane) Quadrant I Quadrant II Quadrant III Quadrant IV Origin P(a, b)

8. Copyright © 2007 Pearson Education, Inc. Slide 1-8 1.1 The TI-83 Viewing Window Limitations in portraying coordinate systems on the calculator screen 1. Resolution 2. Scaling Xmin=-60, Xmax=60, Xscl=1 Xmin=-60, Xmax=60, Xscl=10 Ymin=-40, Ymax=40, Yscl=1 Ymin=-40, Ymax=40,Yscl=10

9. Copyright © 2007 Pearson Education, Inc. Slide 1-9 1.1 Rounding Numbers Mode Setting Display NumberNearest TenthNearest HundredthNearest Thousandth 1.37821.41.381.378 201.6666201.7201.67201.667.0819.1.08.082

10. Copyright © 2007 Pearson Education, Inc. Slide 1-10 1.1 Roots Calculators have the ability to express numbers like: Other special keys:

11. Copyright © 2007 Pearson Education, Inc. Slide 1-11 1.1 The Distance Formula Pythagorean Theorem: Q (x1, y2)Q (x1, y2) d

12. Copyright © 2007 Pearson Education, Inc. Slide 1-12 1.1 Example Using the Distance Formula Find the length of the line segment that joins the points P(  8, 4) and Q(3,  2). Solution:

13. Copyright © 2007 Pearson Education, Inc. Slide 1-13 The midpoint of the line segment with endpoints and is Example Find the midpoint M of the segment with endpoints (8,  4) and (  9,6). Solution: 1.1 Midpoint Formula

14. Copyright © 2007 Pearson Education, Inc. Slide 1-14 1.1 Application: Estimating Tuition and Fees In 1998, average tuition and fees at public universities and colleges were $3293, whereas they were $5132 in 2004. Use the midpoint formula to estimate tuition and fees in 2001. Compare it to the actual value of $4221. Notice that 2001 lies midway between 1998 and 2004. Therefore we can use the midpoint formula. The midpoint formula estimates tuition and fees at public colleges and universities to be $4212.50 in 2001. This is within $10 of the actual value.