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Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Inequalities
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Fractions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Powers
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Slope
Angles and Degree Measure
   
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The Cartesian Coordinate System

The Cartesian coordinate system consists of two real number lines placed at right angles to each other.

The horizontal number line is called the x-axis.

The vertical number line is called the y-axis.

The axes define a flat surface called the xy-plane.

Every point in the xy-plane has two numbers associated with it.

• The x-coordinate or abscissa tells how far the point lies to the left or right of the y-axis.

• The y-coordinate or ordinate tells how far the point lies above or below the x-axis.

The x-coordinate and the y-coordinate are often written inside parentheses, like this: (x, y).

The first number, x, represents the x-coordinate and the second number, y, represents the y-coordinate.

For example, the point that is 3 units to the right of the y-axis and 6 units below the x-axis is labeled (3, -6).

Because the order in which the pair of numbers is written is important, (x, y) is called an ordered pair. Thus, the point (-6, 3) is not the same as the point (3, -6).

The x-axis and the y-axis intersect at the point (0, 0). This point is called the origin.

The x-axis and the y-axis divide the xy-plane into four regions called quadrants.

Quadrant

I

II

III

IV

Sign of x

positive

negative

negative

positive

Sign of y

positive

positive

negative

negative

A point on an axis does not lie in a quadrant.

Example 1

Find the coordinates of each point labeled on the graph.

Then, state the quadrant in which each point lies.

Solution

Point A has coordinates (2, 5), and lies in Quadrant I.

Point B has coordinates (3, -4), and lies in Quadrant IV.

Point C has coordinates (-5, 3), and lies in Quadrant II.

Point D has coordinates (-6, -2), and lies in Quadrant III.

Point E has coordinates (5, 0). It is not in a quadrant since it lies on the x-axis.

 

Example 2

Plot each point on a Cartesian coordinate system:

a. (5, -4)

b. (-4, 6)

c. (-3, 0)

d. (0, -3)

Solution

The plot the point (5, -4), start at the origin:

• move 5 units to the right;

• then move down 4 units;

• place a dot at this location.

Follow a similar procedure for the other points. Notice the difference between the locations of points (-3, 0) and (0, -3).

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