A.6 
The student will graph linear equations and linear inequalities in two variables, including
b) writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. 

Essential Knowledge and Skills 
 Graph linear equations and inequalities in two variables, including those that arise from a variety of realworld situations.
 Use the parent function y = x and describe transformations defined by changes in the slope or yintercept.
 Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equation.
 Write an equation of a line when given the graph of a line.
 Write an equation of a line when given two points on the line whose coordinates are integers.
 Write an equation of a line when given the slope and a point on the line whose coordinates are integers.
 Write an equation of a vertical line as x = a.
 Write the equation of a horizontal line as y = c.

Essential Understandings 
 Changes in slope may be described by dilations or reflections or both.
 Changes in the yintercept may be described by translations.
 Linear equations can be graphed using slope, x and yintercepts, and/or transformations of the parent function.
 The equation of a line defines the relationship between two variables.
 The graph of a line represents the set of points that satisfies the equation of a line.
 A line can be represented by its graph or by an equation.
 The graph of the solutions of a linear inequality is a halfplane bounded by the graph of its related linear equation. Points on the boundary are included unless it is a strict inequality.
 Parallel lines have equal slopes.
 The product of the slopes of perpendicular lines is 1 unless one of the lines has an undefined slope.


Vertical Articulation 
 SOL 7.15  a) solve onestep inequalities; b) graph solutions on number line
 SOL 8.15  b) solve twostep linear inequalities and graph results on number line; c) identify properties of operations used to solve
 SOL 8.16  graph linear equations in two variables
 SOL AFDA.2  use transformations to write equations, given graph of function (linear/quad/exponential/log)
 SOL AII.6  recognize general shape of function (absolute value/square root/cube root/rational/poly/exponential/ log) families/ convert between graphic and symbolic forms of functions ‐ transformational approach to graphing

Instructional Materials 
 VDOE ESS Lesson: Slope2Slope  Equations and Inequalities (PDF)  Investigating slope of horizontal and vertical lines and graphing a line (Word)
 VDOE ESS Lesson: Transformationally Speaking  Equations and Inequalities (PDF)  Identifying patterns in families of graphs and their equations (Word)
 VDOE ESS Lesson: Transformation Investigation  Equations and Inequalities (PDF)  Investigating the components of the equation of a line (Word)
 VDOE ESS Lesson: Equations of Lines  Equations and Inequalities (PDF)  Writing equations of lines (Word)
 Notes: Writing Equations of Lines Using PointSlope Formula (doc)  Answer Key (pdf)

Real World Lessons 
 Mathalicious: Can Music Kill You?  Is there a relationship between music tempo and heart rate?
 Mathalicious: Datelines  Is the "half plus seven" rule for MayDecember relationships a good one?
 Mathalicious: Domino Effect  How much is Domino's really charging you for pizza…and toppings?
 Mathalicious: Donut Stand  What does a little donut stand in Virginia have to do with rates of change, limits, average and marginal cost?

Practice 
 VDOE ESS: Silent Bingo Game (pdf)
 VDOE ESS: Slope2Slope Puzzle (pdf)  Answer Key (pdf)
 VDOE ESS: SlopeIntercept Cards (pdf)
 Worksheet: Writing Equations of Lines Using PointSlope Formula CW (doc)
 Worksheet: Writing Equations of Lines Using PointSlope Formula HW (doc)

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question: Perpendicular Lines (doc)

Videos 
 Video: PH Writing an Equation in PointSlope Form Using a Point and the Slope
 Video: PH Writing an Equation From Slope and YIntercept
 Video: PH Writing an Equation from a Table in PointSlope Form
 Video: PH Writing a Function from a Table

Explore
Learning 
 DistanceTime and VelocityTime Graphs  Create a graph of a runner's position versus time and watch the runner run a 40yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect realworld meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
 Function Machines 2 (Functions, Tables, and Graphs)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
 Modeling Linear Systems  Activity A  Experiment with a system of two lines representing a cat‑and‑mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
 Slope  Activity B  Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.

Websites 
 Notes:
Writing Equations of Lines  notes on finding
the slope at Purplemath.com
 Notes:
Writing Equations of Lines  Dr. Math explains
how to write the equation of a line going through a point
and a slope at mathforum.org.
 Interactive
Notes: Writing Equations of Lines  lessons
and practice problems at Regentsprep.org
 Interactive: Exploring PointSlope Form  mathlet from GeoGebra

Old Website Links 

Common Core
Standards 
8.EE.5 
8.EE.6 
8.F.3 
8.F.4 
8.SP.3 
ACED.2 
AREI.10 
AREI.12 
FIF.6 
FBF.3 
FLE.2 
SID.7 
