Free Algebra
Miscellaneous Equations
Operations with Fractions
Undefined Rational Expressions
Writing Equations for Lines Using Sequences
Intersections of Lines and Conics
Graphing Linear Equations
Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
The circle
Adding Polynomials
Adding Fractions with Unlike Denominators
Factoring Polynomials
Linear Equations
Powers of Ten
Straight Lines
Dividing With Fractions
Multiplication Property of Equality
Rationalizing Denominators
Multiplying And Dividing Fractions
Distance Between Points on a Number Line
Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
Imaginary Numbers
Values of Symbols for Which Fractions are Undefined
Graphing Equations in Three Variables
Writing Fractions as Decimals
Solving an Equation with Two Radical Terms
Solving Linear Systems of Equations by Elimination
Factoring Trinomials
Positive Rational Exponents
Adding and Subtracting Fractions
Negative Integer Exponents
Rise and Run
Multiplying Square Roots
Multiplying Polynomials
Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Factoring by Grouping
Extraneous Roots
Variables and Expressions
Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
Solving Linear Inequalities
Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions
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Graphing Linear Equations

Objective Learn how to graph linear equations.

The main idea of this lesson is that you can draw the graph of a linear equation once you know two points on the graph, by simply placing a ruler along the two points. It is typically easy to find two points on a graph when it is in one of the standard forms.

Key Idea

If two points on a line are known, then the line can be drawn using a ruler.

Use a straightedge to draw the line going through the two points at (1, 2) and (4, -2).

How do we graph a line that is given to you in the form of an equation?

Find two points on the line.

Graphing Lines in Slope-Intercept Form

Example 1

Graph y = 2 x + 3.


Two points are needed to graph this equation, which is given in slope-intercept form. Since the y-intercept is 3, one point is (0, 3). To find a second point, choose any other x value and compute the corresponding y value. For instance, choose x = 1.

y = 2 x + 3  
y = 2(1) + 3 Replace x with 1.
y = 5  

So the point at (1, 5) is also on the line. Now graph the line as shown on the figure below.

This works for all lines in slope-intercept form. The y-intercept is always given and another point can be generated by substituting any other value for x .


Graphing Lines in Point-Slope Form

Example 2

Graph y - 4 = 3( x - 2).


One point on the line is easily found when an equation is in point-slope form. In this case, it is the point at (2, 4). To find a second point, choose an x value different from 2, say 4, and substitute it into the equation.

y - 4 = 3( x - 2)  
y - 4 = 3(4 - 2) Replace x with 4.
y - 4 = 3(2)  
y - 4 = 6  
y = 10 Add 4 to each side.

So the point at (4, 10) is also on the line. Draw a line going through (2, 4) and (4, 10).

Equations in point-slope form can be graphed by first choosing the given point. Then generate a second point by substituting a different x value, and solving for y.


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