SOL Objective(s):
7.12 The student will represent relationships with tables, graphs, rules, and words.
8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.
8.16 The student will graph a linear equation in two variables.
8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.
8.16 The student will graph a linear equation in two variables.
Previous and Related SOL Objectives: 
Prerequisite Skills:Knowledge of quadrants and how to plot points
How to substitute values for variables Application of order of operations 
Khan Skill Phrases:Equations from Tables
Solving for the YIntercept Graphing Linear Equations Understanding Function Notation Interpreting Linear Relationships 
The Basics and Background Information
7th Grade:
• Rules that relate elements in two sets can be represented by word sentences, equations, tables of values, graphs, or illustrated pictorially.
• A relation is any set of ordered pairs. For each first member, there may be many second members.
• A function is a relation in which there is one and only one second member for each first member.
• As a table of values, a function has a unique value assigned to the second variable for each value of the first variable.
• As a graph, a function is any curve (including straight lines) such that any vertical line would pass through the curve only once.
• Some relations are functions; all functions are relations.
8th Grade:
• A relation is any set of ordered pairs. For each first member, there may be many second members.
• A function is a relation in which there is one and only one second member for each first member.
• As a table of values, a function has a unique value assigned to the second variable for each value of the first variable.
• As a graph, a function is any curve (including straight lines) such that any vertical line would pass through the curve only once.
• Some relations are functions; all functions are relations.
• Graphs of functions can be discrete or continuous.
• In a discrete function graph there are separate, distinct points. You would not use a line to connect these points on a graph. The points between the plotted points have no meaning and cannot be interpreted.
• In a graph of continuous function every point in the domain can be interpreted therefore it is possible to connect the points on the graph with a continuous line as every point on the line answers the original question being asked.
• Functions can be represented as tables, graphs, equations, physical models, or in words.
• A linear equation is an equation in two variables whose graph is a straight line, a type of continuous function (see SOL 8.14).
• A linear equation represents a situation with a constant rate. For example, when driving at a rate of 35 mph, the distance increases as the time increases, but the rate of speed remains the same.
• Graphing a linear equation requires determining a table of ordered pairs by substituting into the equation values for one variable and solving for the other variable, plotting the ordered pairs in the coordinate plane, and connecting the points to form a straight line.
• The axes of a coordinate plane are generally labeled x and y; however, any letters may be used that are appropriate for the function.
Any situation with a constant rate can be represented by a linear equation.
• Rules that relate elements in two sets can be represented by word sentences, equations, tables of values, graphs, or illustrated pictorially.
• A relation is any set of ordered pairs. For each first member, there may be many second members.
• A function is a relation in which there is one and only one second member for each first member.
• As a table of values, a function has a unique value assigned to the second variable for each value of the first variable.
• As a graph, a function is any curve (including straight lines) such that any vertical line would pass through the curve only once.
• Some relations are functions; all functions are relations.
8th Grade:
• A relation is any set of ordered pairs. For each first member, there may be many second members.
• A function is a relation in which there is one and only one second member for each first member.
• As a table of values, a function has a unique value assigned to the second variable for each value of the first variable.
• As a graph, a function is any curve (including straight lines) such that any vertical line would pass through the curve only once.
• Some relations are functions; all functions are relations.
• Graphs of functions can be discrete or continuous.
• In a discrete function graph there are separate, distinct points. You would not use a line to connect these points on a graph. The points between the plotted points have no meaning and cannot be interpreted.
• In a graph of continuous function every point in the domain can be interpreted therefore it is possible to connect the points on the graph with a continuous line as every point on the line answers the original question being asked.
• Functions can be represented as tables, graphs, equations, physical models, or in words.
• A linear equation is an equation in two variables whose graph is a straight line, a type of continuous function (see SOL 8.14).
• A linear equation represents a situation with a constant rate. For example, when driving at a rate of 35 mph, the distance increases as the time increases, but the rate of speed remains the same.
• Graphing a linear equation requires determining a table of ordered pairs by substituting into the equation values for one variable and solving for the other variable, plotting the ordered pairs in the coordinate plane, and connecting the points to form a straight line.
• The axes of a coordinate plane are generally labeled x and y; however, any letters may be used that are appropriate for the function.
Any situation with a constant rate can be represented by a linear equation.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Describe and represent relations and functions, using tables, graphs, rules, and words. Given one representation, students will be able to represent the relation in another form.
• Graph in a coordinate plane ordered pairs that represent a relation.
• Describe and represent relations and functions, using tables, graphs, words, and rules. Given one representation, students will be able to represent the relation in another form.
• Relate and compare different representations for the same relation.
• Construct a table of ordered pairs by substituting values for x in a linear equation to find values for y.
• Plot in the coordinate plane ordered pairs (x, y) from a table.
• Connect the ordered pairs to form a straight line (a continuous function).
• Interpret the unit rate of the proportional relationship graphed as the slope of the graph, and compare two different proportional relationships represented in different ways.
• Describe and represent relations and functions, using tables, graphs, rules, and words. Given one representation, students will be able to represent the relation in another form.
• Graph in a coordinate plane ordered pairs that represent a relation.
• Describe and represent relations and functions, using tables, graphs, words, and rules. Given one representation, students will be able to represent the relation in another form.
• Relate and compare different representations for the same relation.
• Construct a table of ordered pairs by substituting values for x in a linear equation to find values for y.
• Plot in the coordinate plane ordered pairs (x, y) from a table.
• Connect the ordered pairs to form a straight line (a continuous function).
• Interpret the unit rate of the proportional relationship graphed as the slope of the graph, and compare two different proportional relationships represented in different ways.
Vocabulary and Things to Know:slope intercept form
slope yintercept independent variable dependent variable domain range rise over run relationship relation function function table 
Be Able To:rewrite an equation
solve a twostep equation identify parts of slopeintercept form: DV, slope, IV, yintercept identify aspects of graph: slope, yintercept plot points graph points from an equation graph points from a function table create function table from equation create function table from graph create equation from two points create equation from function table rewrite an equation in standard form to an equation in slopeintercept form 
The topic: What is it and what will we learn?
Function equations/rules, function tables and function graphs present the same information, just differently, and the information shows a dependable pattern.
Video and Website Resources:
Information posted by a teacher in Ohio via PowerPoint with clear information on what relations are vs. functions.
