Home›Lesson Plans›Mathematics›Expressions & Equations · Grade 8

Slope & Linear Equations: y = mx + b

Students learn to read and graph lines using slope-intercept form — discovering that the slope (m) sets the steepness and direction, and the y-intercept (b) sets where the line crosses the y-axis.

Grade 8Linear50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find the slope of a line (rise over run).
  • ✓Identify the y-intercept.
  • ✓Graph a line from y = mx + b.
  • ✓Write the equation of a line.
Essential Question

Every straight line can be captured in one short equation, y = mx + b. What do the m and the b actually do?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Line Grapher

Project this and change the slope and y-intercept. Watch the line move — m controls the steepness, b slides it up and down.

📈 Change m and b — watch the lineTry it
Slope m: 1
y-intercept b: 0

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — The Line’s DNA

5 min

Two numbers can describe any straight line — which two?

👩‍🏫 Teacher Moves

  • Show several lines.
  • Ask what makes them different.
  • Set the goal: slope-intercept form.

🎒 Student Actions

  • Compare the lines.
  • Find the differences.
  • Predict the two numbers.
2

I Do — m and b

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Define slope = rise over run.
  • Define the y-intercept.
  • Graph y = mx + b.

🎒 Student Actions

  • Find the slope.
  • Find the intercept.
  • Graph the line.
3

We Do — Graph Together

13 min

Class drives the Line Grapher.

👩‍🏫 Teacher Moves

  • Change m and b; observe.
  • Connect m to steepness.
  • Connect b to the crossing point.

🎒 Student Actions

  • Set m and b.
  • Read the line.
  • Explain each.
4

You Do — On Your Own

12 min

Students graph lines.

👩‍🏫 Teacher Moves

  • Assign lines to graph.
  • Find slope and intercept from a graph.
  • Write an equation.

🎒 Student Actions

  • Graph lines.
  • Find m and b.
  • Write equations.
5

Close — Close

5 min

One line.

👩‍🏫 Teacher Moves

  • Give an equation; graph it.
  • State m and b.
  • Hand out the exit ticket.

🎒 Student Actions

  • Graph the line.
  • State m and b.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
8.EE.6

Use similar triangles to explain slope; derive y = mx + b.

CCSS
8.F.3

Interpret y = mx + b as defining a linear function whose graph is a straight line.

CCSS
8.EE.5

Graph proportional relationships and interpret slope as a unit rate.

CCSS
8.F.4

Construct a function to model a linear relationship.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Trace rise and run on a graph.
  • Sentence frame: “The slope is ___; the line crosses at ___.”
  • Color the intercept.

Support & Access

IEP / 504
  • Start with positive whole-number slopes.
  • Highlight the y-intercept.
  • Graph one point at a time.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find slope from two points.
  • Compare steepness of two lines.
  • Write an equation from a real situation.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Line Grapher
  • 📐Graph paper
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

slopethe steepness of a line (rise over run)y-interceptwhere a line crosses the y-axislinearforming a straight linerisevertical changerunhorizontal changeslope-intercept formy = mx + bcoefficientthe number multiplying a variablegrapha picture of an equation
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
In y = 3x + 2, what is the slope and the y-intercept?
Slope = 3, y-intercept = 2.
QUESTION 2
If a line has slope 2, how does it change as you move 1 unit right?
It goes up 2 units.
QUESTION 3
What does the y-intercept tell you?
Where the line crosses the y-axis (the value of y when x = 0).

Going deeper? Slope from two points.

Have students find the slope between two points using (y₂ − y₁) ÷ (x₂ − x₁), then write the full equation. A printable slope sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Slope & Linear EquationsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Slope & Linear EquationsQuiz
Score: 0
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Slope & Linear EquationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: coefficient, graph, linear, rise, run, slope, slope-intercept form, y-intercept
  1. y = mx + b
  2. horizontal change
  3. vertical change
  4. forming a straight line
  5. the number multiplying a variable
  6. a picture of an equation
  7. where a line crosses the y-axis
  8. the steepness of a line (rise over run)

Part B · Show what you learned

  1. In y = 3x + 2, what is the slope and the y-intercept?
  2. If a line has slope 2, how does it change as you move 1 unit right?
  3. What does the y-intercept tell you?
Answer key — Part A: 1) slope-intercept form · 2) run · 3) rise · 4) linear · 5) coefficient · 6) graph · 7) y-intercept · 8) slope
Part B: 1) Slope = 3, y-intercept = 2. 2) It goes up 2 units. 3) Where the line crosses the y-axis (the value of y when x = 0).