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Rotating a Parabola
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The Square of a Binomial
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Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Algebra
Order of Operations
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The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Factoring
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Functions and Graphs
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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
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Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Fractions
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Solving Rational Inequalities with a Sign Graph
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Order of Operations
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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
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Multiplying and Dividing Complex Numbers
Properties of Exponents
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The Quadratic Formula
Writing a Quadratic with Given Solutions
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Combining Like Radical Terms
Solving Systems of Equations Using Substitution
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Product of a Sum and a Difference
Solving First Degree Inequalities
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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.

Solution

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.

Solution

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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