Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
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 real-world situations.
  • Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept.
  • 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 y-intercept may be described by translations.
  • Linear equations can be graphed using slope, x- and y-intercepts, 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 half-plane  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
  1. SOL 7.15 - a) solve one-step inequalities; b) graph solutions on number line
  2. SOL 8.15 - b) solve two-step linear inequalities and graph results on number line; c) identify properties of operations used to solve
  3. SOL 8.16 - graph linear equations in two variables
  4. SOL AFDA.2 - use transformations to write equations, given graph of function (linear/quad/exponential/log)
  5. 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
  1. VDOE ESS Lesson: Slope-2-Slope - Equations and Inequalities (PDF) - Investigating slope of horizontal and vertical lines and graphing a line (Word)
  2. VDOE ESS Lesson: Transformationally Speaking - Equations and Inequalities (PDF) - Identifying patterns in families of graphs and their equations (Word)
  3. VDOE ESS Lesson: Transformation Investigation - Equations and Inequalities (PDF) - Investigating the components of the equation of a line (Word)
  4. VDOE ESS Lesson: Equations of Lines - Equations and Inequalities (PDF) - Writing equations of lines (Word)
  5. Notes: Writing Equations of Lines Given a Graph (doc) | Answer Key (pdf)
Real World Lessons
  1. Mathalicious: Can Music Kill You? - Is there a relationship between music tempo and heart rate?
  2. Mathalicious: Datelines - Is the "half plus seven" rule for May-December relationships a good one?
  3. Mathalicious: Domino Effect - How much is Domino's really charging you for pizza…and toppings?
  4. Mathalicious: Donut Stand - What does a little donut stand in Virginia have to do with rates of change, limits, average and marginal cost?
  1. VDOE ESS: Silent Bingo Game (pdf)
  2. VDOE ESS: Slope-2-Slope Puzzle (pdf) | Answer Key (pdf)
  3. VDOE ESS: Slope-Intercept Cards (pdf)
  4. Worksheet: Writing Equations of Lines Given a Graph CW (doc)
  5. Worksheet: Writing Equations of Lines Given a Graph HW (doc)
  1. SOL Mini Quiz
  1. Video: PH Writing an Equation From a Graph
  2. Video: PH Writing an Equation from a Graph in Point-Slope Form
Explore Learning
  1. Distance-Time and Velocity-Time Graphs - Create a graph of a runner's position versus time and watch the runner run a 40-yard 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 real-world 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.
  2. 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 pre-set 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.
  3. 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.
  4. 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.
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Common Core Standards