A.6a 
The student will graph linear equations and linear inequalities in two variables, including
a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined. 

Essential Knowledge and Skills 
 Find the slope of the line, given the equation of a linear function.
 Find the slope of a line, given the coordinates of two points on the line.
 Find the slope of a line, given the graph of a line.
 Recognize and describe a line with a slope that is positive, negative, zero, or undefined.

Essential Understandings 
 Changes in slope may be described by dilations or reflections or both.
 The slope of a line represents a constant rate of change in the dependent variable when the independent variable changes by a constant amount.
 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: Slippery Slope  Equations and Inequalities (PDF)  Writing equations of lines (Word)
 VDOE ESS Lesson: The Submarine  Equations and Inequalities (PDF)  Investigating slope as rate of change (Word)
 VDOE ESS Lesson: Equations of Lines  Equations and Inequalities (PDF)  Writing equations of lines (Word)
 Notes: Slope (doc)  Answer Key (pdf)

Real World Lessons 
 Slope for the
Mathematically Inclined worksheet (doc)  (pdf)  Slope
Application video (mov)
 Lab Activity 
Finding Slope with Stairs (pdf)
 Slope Exploration
worksheet (doc)  (pdf)

Practice 
 VDOE ESS: Silent Bingo Game (pdf)
 VDOE ESS: Slope2Slope Puzzle (pdf)  Answer Key (pdf)
 VDOE ESS: SlopeIntercept Cards (pdf)
 Worksheet: Slope CW (doc)
 Worksheet: Slope HW (doc)
 ExamView Quiz: Slope
 Prentice Hall Quiz

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question: Walking a Path (doc)

Videos 
 Video: PH Finding slope using rise/run
 Video: PH Finding slope using coordinates
 Video: PH Finding the slope of horizontal or vertical line

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:
Using Slope to Graph Lines  notes on graphing
using slope at Purplemath.com
 Notes:
Slope of Lines  notes on finding slope
at Purplemath.com
 Interactive:
Slope Activity  adjust the line on a graph
to identify the correct slope.
 Interactive: Investigating Horizontal Lines  mathlet from GeoGebra
 Interactive: Investigating Vertical Lines  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 
