Elimination Using Multiplication
Prime Factors
Equations Involving Rational Exponents
Working with Percentages and Proportions
Rational Expressions
Interval Notation and Graphs
Simplifying Complex Fractions
Dividing Whole Numbers with Long Division
Solving Compound Linear Inequalities
Raising a Quotient to a Power
Solving Rational Equations
Solving Inequalities
Adding with Negative Numbers
Quadratic Inequalities
Dividing Monomials
Using the Discriminant in Factoring
Solving Equations by Factoring
Subtracting Polynomials
Cube Root
The Quadratic Formula
Multiply by the Reciprocal
Relating Equations and Graphs for Quadratic Functions
Multiplying a Polynomial by a Monomial
Calculating Percentages
Solving Systems of Equations using Substitution
Comparing Fractions
Solving Equations Containing Rational Expressions
Factoring Polynomials
Negative Rational Exponents
Roots and Radicals
Intercepts Given Ordered Pairs and Lines
Factoring Polynomials
Solving Linear Inequalities
Mixed Expressions and Complex Fractions
Solving Equations by Multiplying or Dividing
The Addition Method
Finding the Equation of an Inverse Function
Solving Compound Linear Inequalities
Multiplying and Dividing With Square Roots
Exponents and Their Properties
Equations as Functions
Factoring Trinomials
Solving Quadratic Equations by Completing the Square
Dividing by Decimals
Lines and Equations
Simplifying Complex Fractions
Graphing Solution Sets for Inequalities
Standard Form for the Equation of a Line
Checking Division with Multiplication
Elimination Using Addition and Subtraction
Complex Fractions
Multiplication Property of Equality
Solving Proportions Using Cross Multiplication
Product and Quotient of Functions
Quadratic Functions
Solving Compound Inequalities
Operating with Complex Numbers
Equivalent Fractions
Changing Improper Fractions to Mixed Numbers
Multiplying by a Monomial
Solving Linear Equations and Inequalities Graphically
Dividing Polynomials by Monomials
Multiplying Cube Roots
Operations with Monomials
Properties of Exponents
Mixed Numbers and Improper Fractions
Equations Quadratic in Form
Simplifying Square Roots That Contain Whole Numbers
Dividing a Polynomial by a Monomial
Writing Numbers in Scientific Notation
Solutions to Linear Equations in Two Variables
Solving Linear Inequalities
Multiplying Two Mixed Numbers with the Same Fraction
Special Fractions
Solving a Quadratic Inequality
Parent and Family Graphs
Solving Equations with a Fractional Exponent
Evaluating Trigonometric Functions
Solving Equations Involving Rational Expressions
Laws of Exponents
Multiplying Polynomials
Vertical Line Test
Solving Inequalities with Fractions and Parentheses
Multiplying Polynomials
Solving Quadratic and Polynomial Equations
Extraneous Solutions
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Solving Linear Equations and Inequalities Graphically

The Equation of a Linear Equation

 A linear equation written in slope-intercept form always follows the pattern:

y = m · x + b,

where the letter x represents that values of the input, the letter y represents that values of the output and the letters m and b represent fixed numbers. The number represented by m is called the slope and the number represented by b is called the intercept.

You can find formulas for linear equations by hand (for example if you are given the coordinates of two points and asked to find the equation of the line that joins them) or by linear regression.


The Idea of Solving a Linear Equation Graphically

When you have a linear equation, and know the value of the output, you can solve the equation to find the corresponding input value. This is sometimes called solving the equation for x.

One way of thinking about the process of solving a linear equation like:

2 · x +1= 9,

 is that you are trying to find the x-coordinate of the point where the line y = 2 · x +1 reaches a height of 9 units (see Figure 1, below). The x-value of the point where the slanted line represented by the equation y = 2 · x +1 and the horizontal line represented by the equation y = 9 is the solution of the linear equation 2 · x +1= 9.

Figure 1: The solution of a linear equation is the x-coordinate of the intersection point.


The Idea of Solving a Linear Inequality

A linear inequality is a lot like a linear equation, except that the equals sign is replaced by less than (<), greater than (>), less than or equal to or greater than or equal to . For example:

-2 · x + 3 11.

When you solve an inequality, the idea is to re-arrange the inequality to make x the subject. Unlike solving an equation, when you solve an inequality, you will usually get an interval of x-values as your solution, rather than a single x-value.

You can solve a linear inequality by breaking it down into two separate equations, just as you did for linear equations. For example, to solve the linear inequality:

-2 × x + 3 11,

what you are trying to do is find out when the graph of the slanted line y = -2 · x + 3 is as high (or higher) than the graph of the perfectly horizontal line y = 11.

Figure 2: The solution of a linear inequality is the interval of x-values before or after the intersection point. If the inequality is >= or <= then the interval will also include the x-coordinate of the intersection point.

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