EET 109 Math January 28, 2016 Week 4 Day 2

Three traveling salesman stop at a hotel for the night, they ask how much is a room. The manager says the room is $30. Each man puts a $10 dollar bill on the counter, they get the key and go to their room. The manager notices that he made a mistake, the room is only $25 not $30. He gives five $1 dollar bills to his assistant to return to the gentleman. The assistant walks to the room thinking that he can't give $5 dollars to 3 people. He gets to the room and gives each man one dollar back and keeps two for himself. Each man(3) spent $9=$27 The assistant kept $2 That's a total of $29! What happen to the last dollar?

4.1 Functions 4.2 Graphing Equations 4.3 The Straight Line 4.4 Parallel and Perpendicular Lines 4.5 The Distance and Midpoint Formulas

Week 3 Chapter 1 Fundamental Concepts 1.6 Algebraic Expressions 1.7 Exponents and Radicals 1.8 Multiplication of Algebraic Expressions 1.9 Division of Algebraic Expressions 1.10 Linear Equations 1.13 Applications Involving Linear Equations

Week 5 Chapter 5 Factoring and Algebraic Fractions 5.1 Special Products 5.2 Factoring Algebraic Expressions 5.5 Multiplication Division of Algebraic Expressions 5.6 Addition and Subtractions of Algebraic Expressions 5.8 Equations with Fractions

1.11 FORMULAS page 42 Solving a formula means to isolate a given letter on one side of the equal sign. We solve formulas using the same principles used solving equations.

Page 133

Prove

Chapter 4 Equations and Their Graphs Functions and their equations can be graphed. Page 145

4.1 FUNCTIONS page 145 Equations can state relationships between x and y.

5 = 2x + 1x = 2 y = 2x + 1 x, y 2, 5 3, 7 4, 9

ordered pairs of numbers in the form x y Independent variableDependent variable InputsOutputs Domain Range

4.1 FUNCTIONS page 147 Functional notation: Stated as: “f of x”

Y = f (x) This is f of X NOT f times x. Inputs Outputs

Y = f (x) X Y 2, 5 3, 7 4, 9

4.2 GRAPHING EQUATIONS page 152 Plotting points from order pairs. Plotting is fundamental to correct graphs.

From (ordered) pairs to plotting points to graphing.

4.2 GRAPHING EQUATIONS PAGE 150 Doug’s tips for graphing a function. For X use -1, 0, 1, 2 The pair will be near the origin. The pair will allow for possible negative and positive outcomes. The numbers are mathematically easy to work with.

Page 152 A linear equation with two unknowns is an equation of degree one in the form with a and b not both 0. Degree one means no exponents.

4.2 GRAPHING EQUATIONS page 152 The graph of a linear equation is a straight line. Therefore, two ordered pairs are sufficient to graph it, since two points determine a straight line. However, finding a third point provides good insurance against a careless error.

4.2 GRAPHING EQUATIONS page 152 The graph of an equation that is not linear is usually a curve of some kind and requires several points to sketch a smooth curve.

4.2 GRAPHING EQUATIONS page 152

Y-intercept

Page 154 Solving for y = 0 This graphically means finding the point or points, if any, where the graph crosses the y axis. x y (0, 2)

Y intercept may be solved graphically.

4.3 THE STRAIGHT LINE Page 162 Y intercept may be solved mathematically. (section 4.3)

Slope

4.3 THE STRAIGHT LINE page 159 The slope of a line is the ratio of the difference of the y-coordinates of any two points on the line to the difference of their x-coordinates.

4.3 THE STRAIGHT LINE page 159 The slope of a line.

Any 2 ordered pair can be used.

X, Y 1, 2 6, 4

Split the ordered pairs: Don’t divide one pair by the other. Don’t have x - y divided by x - y

X, Y 1, 2 6, 4

Rise over run is not in the text.

If a line has positive slope, then the line slopes upward from left to right (“rises”). If a line has negative slope, then the line slopes downward from left to right(“falls”).

If the line has zero slope, then the line is horizontal (“flat”). y 2 – y 1 = 0

If the line is vertical, then the line has undefined slope because of 0.

4.3 THE STRAIGHT LINE page 161 Point-Slope form is a simple manipulation of the slope formula.

Solve for: y 2 – y 1 =

4.3 THE STRAIGHT LINE page 161 This allows us to find the equation for a line given the slope of the line and a point (ordered pair).

Find the equation for a line with point (-1, 2) and a slope of 3. Substitution Multiply by 3 Add 2 to both sides

At the y intercept x will equal 0. x y (0, b) X = zero b= the y intercept

Point (ordered pair) slope form. Slope from 2 points (ordered pairs). Slope y-intercept Form. b = y intercept

Page 163 Zero slope.

Page 164 Undefined slope.

More than one line.

4.4 PARALLEL AND PERPENDICULAR LINES Page 166

=

Slope is undefined.

4.4 PARALLEL AND PERPENDICULAR LINES Page 166

4.5 THE DISTANCE AND MIDPOINT FORMULAS page 170

4.5 THE DISTANCE AND MIDPOINT FORMULAS page 171