Equations and Inequalities of Two Variables and Functions for Algebra from Elevated Math

These 19 lessons provide initial instruction or intervention on linear equations and inequalities of two variables and functions.

The first 4 lessons define those equations and their solutions, provide instruction on graphing those equations and inequalities, and have students to apply their knowledge when solving consumer/business problems.
A7.1 Defining Linear Equations of Two Variables and Their Solutions
A7.2 Graphing Linear Equations of Two Variables
A7.3 Graphing Linear Inequalities of Two Variables
A7.4 Solving Consumer/Business Problems Using Linear Equations and Inequalities of Two Variables

The next four lessons have students find the slope of a line, write equations of lines, and transform an equation into slope-intercept form, along with other specific objectives involving slope.
Slope is used extensively in the real world. For example, knowing the slopes of roads, roofs, ski slopes, wheelchair ramps, and lawn mower handles can be very useful. If the slope is too great, the structure can become dangerous or ineffective. These four lessons are preparation for a more advanced math course, calculus, in which students find the slope of lines that are tangent to a curve.
A8.1 Finding Slope
A8.2 Writing Equations of Lines, Given the Slope and y-Intercept
A8.3 Writing Equations of Lines, Given a Point and the Slope or Two Points
A8.4 Solving Linear Equations in Two Variables When Parameters Are Changed

A function is an equation in which any x that can be inserted into the equation yields exactly one y from the equation. The skill of writing equations in function notation and evaluating functions will be used throughout mathematics education, as in trigonometry when trig functions are used to find the sides and angles of triangles. The six lessons of this module provide a basic knowledge of functions.
Functions are used in carpentry and in creating travel schedules and pay schedules. Airfare, car rental rates, international call rates, and recycling payments are computed using functions.
A9.1 Defining Relations and Functions
A9.2 Evaluating Functions
A9.3 Writing Functions from Patterns
A9.4 Graphing Functions
A9.5 Solving Problems Using Functions
A9.6 Evaluating Composite Functions

A system of equations is a set of two or more linear equations that uses the same variables. An ordered pair is a solution to a system of two equations if it satisfies both equations. More specifically, a system of equations consists of two or more equations having variables that represent the same values. For example, the equations 3x + 4y = 5 and 4x + 5y = 6 form a system if x represents the same thing in both equations, y represents the same thing in both equations, and both equations refer to the same context. In order to "solve the system," students must find values for the variables that make both statements true [x = -1; y = 2].
A10.1 Solving Systems of Linear Equations by Graphing
A10.2 Solving Systems of Linear Equations by Elimination
A10.3 Solving Systems of Linear Equations by Substitution
A10.4 Solving Systems of Linear Inequalities by Graphing
A10.5 Solving Problems Using Systems of Liner Equations and Inequalities.

Student print materials and Teachers Notes are available for download at www.elevatedmath.com

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