Algebra Tutorials!  
Monday 24th of June
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Standard Form of a Line

If x students paid $5 each and y adults paid $7 each to attend a play for which the ticket sales totaled $1900, then we can write the equation 5x + 7y = 1900. This form of a linear equation is common in applications. It is called standard form.


Standard Form

The equation of a line in standard form is Ax + By = C, where A, B, and C are real numbers with A and B not both zero.


The numbers A, B, and C in standard form can be any real numbers, but it is a common practice to write standard form using only integers and a positive coefficient for x.


Example 1

Changing to standard form

Write the equation in standard form using only integers and a positive coefficient for x.


Use the properties of equality to get the equation in the form Ax + By = C:

y Original equation
Subtract from each side.
Multiply each side by 4 to get integral coefficients.
-2x + 4y = -3 Distributive property
2x - 4y = 3 Multiply by -1 to make the coefficient of x positive.

To find the slope and y-intercept of a line written in standard form, we convert the equation to slope-intercept form.


Example 2

Changing to slope-intercept form

Find the slope and y-intercept of the line 3x - 2y = 5.


Solve for y to get slope-intercept form:

3x - 2y = 5 Original equation
-2y = -3x + 5 Subtract 3x from each side.
y Divide each side by -2.

The slope is , and the y-intercept is .


Helpful Hint

Solve Ax + By = C for y, to get

So the slope of Ax 6+ By = C is This fact can be used in checking standard form. The slope of 2x - 4y = 3 in Example 2 is , which is the slope of the original equation.

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