Patterns, Functions, and Algebra
Focus: Linear Relationships
The student will graph a linear equation in two variables. 


Essential Knowledge and Skills 
 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.†Revised March 2011

Essential Understandings 
 What types of real life situations can be represented with linear equations? Any situation with a constant rate can be represented by a linear equation.


Vertical Articulation 
 SOL 6.20  graph inequalities on number line
 SOL 7.15ab  solve onestep inequalities; b) graph
solutions on number line
 SOL A.5  solve multistep linear inequalities (2
variables)  a) solve multistep linear
inequalities (algebraically/graphically); b)
justify steps used in solving inequalities; c)
solve realworld problems involving
inequalities; d) solve systems of inequalities

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Graphing Linear Equations (PDF)  Graphing linear equations (Word)
 Notes: Graphing Linear Equations (flipchart)
 Notes: Graphing Linear Equations #2 (flipchart)
 Notes: Graphing Linear Functions (ppt)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 
 Den Meyer: Joulies  Do you think Joulies will work as advertised?

Practice 
 Worksheet: Tables and Relations (pdf)

SelfAssessments 
 SOL 8.16 MiniQuiz: Graphing Linear Equations

Skills 
 Mathematics Assessment Project: A17:Linear Graphs  Apprentice  In this task, you are asked to match equations with linear graphs.
 Graphing: Crawling Crayfish (doc)

Videos 

Explore
Learning 
 Defining a Line with Two Points: Place two points wherever you like. Compute the slope of the line between them. View the equation of that line in slope‑intercept and point‑slope form.
 PointSlope Form of a Line  Activity A: Compare the pointslope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
 SlopeIntercept Form of a Line  Activity A: Compare the slope‑intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
 Standard Form of a Line: Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.

Websites 
 Notes: Graphing Using a Tchart  notes on graphing at Purplemath.com
 Interactive: Slope Slider  manipulate a linear function in the form of f(x) = mx + b at Shodor.org
 Interactive: Graphing Activity  real world activity and lesson used with graphing functions
 Interactive: Graphing Functions  math manipulative at matti.usu.edu that graphs up to 3 functions at a time. Choose the Grapher icon from the list.

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra  The lessons focus on algebraic reasoning. Students explore the relationships found in
number patterns through arithmetic and geometric sequences using variables expressions.. They use modeling to collect data, and they learn to record data so that they can see the
relationship that exists among tables, graphs, words, and equations. (pdf)

Common Core
Standards 
8.EE.5 
8.F.1 
8.F.3 
8.F.4 
8.F.5 
