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Math workbook

Linear Equations and Graphs: Tables, slopes, equations and systems

Grades 9–12Level 4
Cover of Linear Equations and Graphs: Tables, slopes, equations and systems

About this book

See one relationship four ways, then find where two lines meet.

Linear Equations and Graphs helps high-school learners connect tables, graphs, equations and real situations. Four modules move from spotting a constant rate of change, to reading slope and intercept with units, to writing and rearranging equations of lines, to solving systems of two equations. Each module follows the same seven steps: check what you need, a plain explanation, worked examples, guided practice, independent practice, review of earlier learning, and answers with explanations. Contexts include printing costs, service plans and break-even points. An answer key with reasons, common errors and reteaching cues supports parents and teachers.

  • Readiness check with a clear route for where to start
  • Worked examples with every step shown
  • Error-analysis pages built on real misconceptions
  • Cumulative review, exit check and a short retry
  • Explanatory answer key for adults at the back

For learners in grades 9–12 who can solve two-step equations and plot points on a coordinate plane.

Look inside

Page 5 of Linear Equations and Graphs. Step 2, Concept: Linear patterns across representations
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Page 6 of Linear Equations and Graphs. Step 3, Worked Example: Linear patterns across representations
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What this book covers

Covered

  • This book is about one big idea: a linear relationship changes by the same amount for every equal step.
  • You will find and explain slope and intercept with units, write and rearrange equations of lines and formulas, compare parallel and perpendicular slopes, and solve systems of two lines.

Not covered

Not in this book: curved graphs such as parabolas (see Quadratics: Patterns, Graphs, and Solutions), inequalities, lines of best fit for messy data, and systems with three unknowns.

Before you start

If equations or signed numbers feel shaky, start with Expressions and One-Variable Equations or Integer Operations: From Number Lines to Rules.

Things to have

  • Use a pencil and a ruler.
  • A calculator is fine for arithmetic, but show the setup.

Notice

Pictures in this book are simplified learning models. Check answers with the explanations at the back of the book.

The steps in this book

How the steps work
  1. Step 1: Readiness Check

    Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.

  2. Step 2: Concept

    Read a short, clear explanation of the new idea and the words that go with it.

  3. Step 3: Worked Example

    Watch the idea being used, one step at a time, in a worked example.

  4. Step 4: Guided Practice

    Practice with prompts and help cues. The help gets smaller as you get stronger.

  5. Step 5: Independent Practice

    Practice on your own with different kinds of questions, and explain your thinking.

  6. Step 6: Review

    Look back at earlier learning so it stays strong, then check where to go next.

  7. Step 7: Answers and Explanations

    Check your answers. Each answer explains why, names a common mistake, and shows how to fix it.

What is in the book

The modules

  1. Module 1: Linear patterns across representationsPages 5–14
  2. Module 2: Slope and intercept have unitsPages 15–24
  3. Module 3: Write and rearrange linear equationsPages 25–34
  4. Module 4: Intersections answer shared constraintsPages 35–44

Contents

  1. Readiness check, pp. 3–4. Before Module 1. Its table tells you where to start.
  2. Modules, pp. 5–44
  3. Checkpoints, pp. 14, 24, 34, 44. The last page of each module.
  4. Mixed review, pp. 45–48. Questions from across the book, mixed together.
  5. Exit check, pp. 49–50. A last check across the book.
  6. Reflect and repair, p. 51
  7. Try again, p. 52. Fresh questions like those in the exit check.
  8. Further practice, pp. 53–55. More pages of step 5, Independent Practice.
  9. Extra practice, pp. 56–58
  10. Answers and explanations, pp. 59–68. Notes in this part are headed “Why”, “Common mistake” and “Help”.

Before this book

If equations or signed numbers feel shaky, start with Expressions and One-Variable Equations or Integer Operations: From Number Lines to Rules.

Review Integer Operations: From Number Lines to Rules or Multiplying and Dividing Fractions, or ask an adult for a short lesson.

After this book

Next steps after this book: Quadratics and College Algebra: Functions and Graphs.

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