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Solving Linear Equations
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Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Percents
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Algebra
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
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Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
fractions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Quadratics
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Decimals
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
   
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Linear Equations

Recall:

  • Graphing a line.
  • What the graph means.
  • Slope.
  • x - and y -intercepts.

New Stuff:

  • Slope-intercept form of the equation.

The graph of the equation y = mx + b is a straight line with slope m and y -intercept ( 0 ; b ).

Procedure: (Writing an Equation in Slope-Intercept Form)

To write a linear equation in slope-intercept form, solve the equation for y .

Examples:

Write the equations in slope-intercept form. Then find the slope and y-intercept.

1. 8x + 2y = -6

2. -5x + y = 15

  • Using the y -intercept and the slope to draw a graph.

Procedure: (Using the y -intercept and Slope to Graph a Line)

1. Find the slope and write it as a fraction (i.e. if the slope is 2, write it as ).

2. Find the y -intercept and plot it. This is your starting point.

3. From the starting point:

  • If the slope is positive, move up the distance on the top of the fraction and right the distance on the bottom of the fraction to find a second point.
  • If the slope is negative, move DOWN the distance on the tope of the fraction and right the distance on the bottom of the fraction to find a second point.

4. Starting at the second point you found above, repeat the previous step to find a third point.

5. Connect the points with a straight line and extend the line straight in each direction.

Example:

Graph both of the equations in the previous example on the same set of axes.

  • Solving equations graphically.

Procedure: (Solving Equations Graphically)

1. Graph each side of the equation.

2. Find all points of intersection.

3. The x coordinates of the points of intersection are the solutions.

Example:

Solve the equation -4x - 3 = 5x + 15 graphically.

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