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Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
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
Dividing Polynomials
Polynomials
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

Graphing Linear Equations

Graphing Equations Using Two Points Use the equation to find the coordinates of any two points on the line. Draw the line representing the equation by connecting them. The two points chosen can be the x- and y-intercepts.
Graphing Equations Using a Point and the Slope Graph one point and use the slope to find another point by moving the distance of the change in y and then the distance of the change in x from that point. When the equation is in point-slope form, y - y1 = m( x - x1), use the point ( x1, y1) and the slope m. When the equation is in slope-intercept form, y = mx + b, use the point (0, b) and the slope m.

 

Example

Graph -2x + 3y = 9 by using the slope and y -intercept.

Solution

3y = 2x + 9 Solve the equation for y.
Slope-intercept form.
y-intercept: 3 (0, 3) is on the line.
slope of line: Move up 2 units, then right 3 units from that point.

 

Parallel and Perpendicular Lines

Parallel Lines Lines in the same plane that never intersect are called parallel lines. If two nonvertical lines have the same slope, then they are parallel. All vertical lines are parallel.
Perpendicular Lines Lines that intersect at right angles are called perpendicular lines. If the product of the slopes of two lines is -1, then the lines are perpendicular. The slopes of two perpendicular lines are negative reciprocals of each other. In a plane, vertical lines and horizontal lines are perpendicular.

 

Example

Determine whether the graphs of 2 y = -3 x + 4 and 3 y = 2 x - 9 are parallel, perpendicular, or neither.

Solution

Rewrite each line in slope-intercept form to identify its slope.

2 y = -3 x + 3 y = 2 x - 9

Since , these lines are perpendicular.

 

Midpoint of a Line Segment

Midpoint of a Line Segment The midpoint of a line segment is the point that is halfway between the endpoints of the segment. The coordinates of the midpoint of a line segment whose endpoints are at ( x1, y1) and ( x2, y2) are given by

 

Example

The midpoint of a segment is M (2, 3) and one endpoint is B ( -1, 5). Find the coordinates of the other endpoint.

Solution

Let M(2, 3) = (x, y) and B( -1, 5) = ( x1, y1).

Form two equations by setting the x-coordinates equal to each other and the y-coordinates equal to each other.

Coordinates of the other endpoint: (5, 1).

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