# Algebra Help

Need some algebra help? Or just wanting to review some key concepts in algebra? Here are some lessons to get you started on this important branch of math. With these lessons, algebra will no longer be a mystery reserved for the selected few.

An overview of algebra word problems (includes videos and step-by-step solutions) covers the common types of word problems in high school and college prep math and the various techniques for solving them.

Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.

### Types Of Algebra Word Problems

How to Translate Words to Equations?
The following examples, solutions & videos will show you how to solve the types of algebra word problems that are commonly found in algebra assignments, homework & tests. We hope that these examples will help you learn how to approach the different types of algebra word problems.

### Coordinate Geometry & Graphs

• Coordinate Geometry & Graphs

Coordinate Geometry
Coordinate plane, Slope Formula, Equation of a Line, Slopes of parallel lines, Slope of perpendicular lines, Midpoint Formula, Distance Formula

Coordinate Plane
Coordinate plane or Cartesian plane, points on the Cartesian Plane, quadrants.

Slope of a Line
Slope of line from the graph (rise over run), using the slope formula, negative slope, y-intercept

Equation of a Line
Slope-intercept form for the equation of a line, how to write equations in slope-intercept form, how to write equations of horizontal & vertical lines, how to get the equation of a line given two points on the line.

Forms of Linear Equations
Slope-intercept form, the point-slope form, the general form, the standard form, how to convert between the different forms of linear equations.

Graphing Linear Equations
How to graph linear equations by plotting points, how to graph linear equations by finding the x-intercept & y-intercept, how to graph linear equations using the slope & y-intercept.

Slope & Intercept of a Linear Equation
How to graph a linear equation when the equation is given in slope-intercept form or when the equation is given in general form.

Explore the straight line graph Activity to investigate how the change of the slope and y-intercept can affect the straight line graph.

Equation of a Line Parallel to the X-axis or Y-axis
Equation of a Line Given its Slope and a Point on the Line
Equation of a Line Given Two Points on the Line

Slopes of Parallel & Perpendicular Lines
How to determine if two lines are parallel or perpendicular when given their slopes, how to find the equation of a line given a point on the line & a line that is parallel or perpendicular to it, how to find parallel or perpendicular lines using Standard Form.

Midpoint Formula
Midpoint formula, how to find the midpoint given two endpoints, how to find one endpoint given the midpoint & another endpoint, how to proof the midpoint formula.

Distance Formula
How to derive the distance formula from the Pythagorean Theorem, how to use the distance formula.

• Linear Inequalities & Linear Programming

Graphing Linear Inequalities
Graph of linear inequalities, how to graph linear inequalities, how to graph systems of linear inequalities.

Graphing Inequalities

Linear Programming
Linear programming, how to use linear programming to solve word problems.

• Functions & Graphs

Different forms of quadratic functions, general form, factored form, vertex form, convert from general form to factored form, convert from the general form to the vertex form using the vertex formula, convert from the general form to the vertex form using completing the square.

How to graph of quadratic functions by plotting points, how to graph quadratic function of the form y = ax2, the properties of the graph y = ax2, how to graph a quadratic function given in general form, how to graph a quadratic function given in factored form, how to graph a quadratic function given in vertex form.

How the solutions of a quadratic equation is related to the graph of the quadratic function, how to use the graphical method to solve quadratic equations.

Graphing Cubic Functions
How to graph of cubic functions by plotting points, how to graph cubic functions of the form y = a(xh)3 + k.

Graphing Exponential Functions
How to graph exponential functions by plotting points, the characteristics of exponential functions, how to use transformations to graph an exponential function.

### A Series Of Mathematics Video Lessons By Portland Community College - Algebra Review

• Algebraic Expressions & Equations

Expressions & Equations
Introduction To Algebraic Expressions:
- What is an algebraic expression?
- The vocabulary of algebraic expressions
- The geometry of algebraic expressions
- Combining like terms
- Simplify Algebraic Expressions using the distributive property

An Introduction To Equations:
- Why do we write equations?
- What is an equation? What is a solution to an equation?
- Different types of equations

Introduction To Linear Equations:
- What makes an equation linear?
- Using addition property and multiplication property of equality to solve linear equations.
- Checking solutions.

• Linear Equations & Inequalities

Equations & Inequalities
Solve Linear Equations:
- Properties of equality Equations that involve simplification
- Equations containing fractions.
- A general strategy for solving linear equations

Solution Sets:
- Solutions vs solution sets: graphing solution sets
- Identity equations & inconsistent equations; the empty set; the set of real numbers
- Solution sets for linear equations
- Solutions & solution sets to inequalities; set builder notation

Solve Linear Inequalities That Have Only One Variable:
- Solution sets to inequalities.
- The addition property of inequalities
- The positive multiplication property of inequalities
- The negative multiplication property of inequalities

• Literal Equations, Percents & Mixtures

Word Problem, Percents, Mixtures
Literal Equations:
- Definition
- Solve for a variable
- Modeling & solving word problems using algebra
- Word problems with one unknown
- Word problems with more than one unknown
- An alternative strategy for thinking through the problem

Working with percents:
- Percents, fractions & decimals
- A basic blueprint for percent questions
- A bona-fide application involving percents

Problem Solving Mixtures & solutions:
- The fundamental concept of mixing it up in mixture problems.
- Examples.

• Ratio & Geometry

Ratio & Geometry
Ratio, Proportions & Rates:
- Ratio, rates & rational numbers, Proportions

Problem Solve With Proportions:
- Direct proportions
- Inverse or reciprocal proportions
- Proportions in geometry

2-Dimensional Geometry - Introduction To Perimeter & Area
- Perimeter, circumference & linear units
- Area & Square Units.

3-Dimensional Geometry:
- Introduction to volume & surface area
- Volume & surface area formulas

• Equations & Slopes

Equations & Slopes
Equations With Two Variables:
- Solutions sets to equations with one variable
- Solution sets to linear inequalities with one variable
- Solution sets to equations with two variables

Plotting Solutions From A Table:
- Table of values, Application

Slope:
- Slope between two points, Slope of a line
- Positive slope, negative slope, zero slope

Determining Slope From Tables:
- Computing “rise over run”" given a table of data
- Determining whether a table of data describes a linear relationship
- Generating a table of data from a verbal description

• Slopes & Lines

Slopes & Lines
Slope Sense:
- Sign on slope
- Magnitude of slope
- Parallel lines

Comparing Slopes:
- Perpendicular lines
- Vertical lines, Horizontal lines
- Summary of slopes

Graphing Lines Using Intercepts:
- Three forms of the equation for a line Intercepts
- Standard Form
- Slope-intercept form

Matters Of Scale:
- Slippery slope
- Broken scale

• Linear Equations

Linear Equations
Finding Equations Of Lines:
- Given slope & vertical intercept
- Given both intercepts, Applications

Slope-Intercept Form:
- Find the equation of a line given the slope & a point on the line
- Applications of linear equations

Point-Slope Form Of A Linear Equation:
- Point-slope form
- Finding a linear equation given two points on a line
- Finding a linear equation given a graph of a line
- Applications of Linear Equations

• Linear Inequalities

Linear Inequalities
Linear Inequalities In Two Variables:
- Linear inequalities of the form x > C
- Linear inequalities of the form y > C
- Linear inequalities of the form y > mx + b
- Applications of Linear Inequalities in two variables

Course Review & Summary:
- Linear Equations
- Linear Modeling

• Systems Of Equations

Systems Of Equations
Solve Systems Of Linear Equations:
- What is a solution to a Systems of Linear Equations in Two Variables?
- Solve Systems of Linear Equations by Graphing
- Solve Systems of Linear Equations in Two Variables by Substitution
- When is Substitution the best method?
- Special Cases
- Three Common Solution Methods

• Systems Of Equations Applications

Systems Of Equations Applications
Applications Involving Systems Of Linear Equations In Two Variables:
- A Word Problem
- Applications involving money

Geometry, Systems & Substitutions:
- Linear Systems based in Geometry
- Using Substitution to find new formulas from old

• Polynomials

Polynomials
Polynomials:
- What is a polynomial? Definitions
- Evaluating polynomials

Multiplying Polynomials:
- Multiply monomials
- The distributive property
- Multiply binomials

Multivariable Product:
- Multiply polynomials by monomials
- FOIL
- Special products, Products involving polynomials with more than two terms

The Geometry Of Polynomial Multiplication: - Basic geometry examples & applications
- Perfect square trinomials

• Exponents

Exponents
Exponents:
- Three important rules of exponents
- Two important definitions of exponents
- An alternate definition of a polynomial
- Examples
- Find a strategy that will work for you
- One last exponent rule

• Scientific Notation

Scientific Notation
- Powers of ten & place value
- Computations using scientific notation
- Astronomical Calculations

• Factoring

Factoring
- An introduction to factoring
- What is factoring?
- The greatest common factor
- Factor out the greatest common factor
- Factor Binomials of the form x2 + bx + c

- Recognizing patterns that emerge from FOIL
- Guess & check, Factor binomials
- Factor Trinomials by grouping
- Factor second-degree trinomial expressions
- Factor multivariable trinomial expressions

• Factor Trinomials

Factor Trinomials
- Special form factorization Perfect Square Trinomials
- Difference of Squares, Sum or difference of cubes
- Discuss what went wrong in the following ?factorizations?

- Solve Quadratic Equations by Factor
- What is a quadratic equation?
- The zero-product principle

• Finding square roots

Finding square roots
- Simplify Square Roots Rationalizing the denominator
- Solve Quadratic Equations using the square root property
- Solution sets to quadratic equations
- What is the quickest method to solve a quadratic equation?

- Working with formulas
- Graphs of Parabolas
- The axis of symmetry & the vertex

- The Graphing Form of Quadratic Equations in Two Variables
- Applications involving maxima & minima

• Functions & Review

Functions
- Relations, Domain, Range
- Definition of a Function, Function Notation
- Numerical & Graphical Representation of Functions

Course Review:
- Systems of Equations, Exponents & Square Roots
- Questions on Systems of Equations, exponents, square roots, scientific notation, quadratics

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 