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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Writing Linear Equations

Writing linear equations for a graph.

If the graph is nonvertical:

• Determine the y -intercept ( b)

• Determine the slope using rise over run (m )

• Write a linear equation using y = mx + b and replacing m and b with the values you found

If the graph is vertical:

• Determine the x -intercept ( a )

• Write a linear equation using x = a and replacing a with the value you found

 

Writing a linear equation for a given point and slope.

Example

Write a linear equation with a slope of 2 and containing the point (-3, 5).

Use the point-slope form for a linear equation: y - y 1 = m ( x - x 1 )

Substitute the values into the equation as follows: y - 5 = 2( x - (-3))

y - 5 = 2 x + 6

y = 2 x + 11

 

Writing a linear equation with 2 given points:

Example

Given (0, 2) and (4, 5), write a linear equation

 

First determine the slope of the line:

Then use the point-slope form to write the equation. Use either point.

 

Writing a Linear Equation for a graph described by a 2nd equation.

• In all cases, find the slope and a point on the line to solve.

Example

A line passes through the point (3, 2) and has the same slope as the the line for y = -2x + 5.

m = -2 for both lines so...

y - 2 = -2( x - 3)

y - 2 = -2x + 6

y = -2 x + 8

Example

A line passes through the point (-4, -2) and is parallel to the line 2 x + 4 y = 4.

Find the slope of the line 2 x + 4 y = 4

4 y = -2 x + 4

therefore

 

Example

A line passes through the point (2, 5) and is perpendicular to the line - x + 3 y = -2.

Find the slope of the line - x + 3 y = -2.

3 y = x - 2  

If the slope of - x + 3 y = -2 is then the slope of the perpendicular is -3 so...

y - 5 = -3( x - 2)

y - 5 = -3 x + 6

y = -3 x + 11

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