Lesson 10 | Linear Relationships | 8th Grade Mathematics

Objective

Write linear equations from graphs in the coordinate plane.

Common Core Standards

Core Standards

The core standards covered in this lesson

8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Expressions and Equations

8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Functions

8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Identify the slope and $$y$$-intercept of a line graphed in a coordinate plane.
Given a graph of a line, write a linear equation in slope-intercept form.
Match graphs of equations and equations written in slope-intercept form.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Anchor Problem #3 is an optional matching game activity that requires preparation in advance of the lesson.

Lesson Materials

Optional: Matching game (1 per pair of students)

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

What is an equation of the line represented in the graph below?

Guiding Questions

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Problem 2

Four lines were used to define the edges of the trapezoid shown below.

Write an equation for each line described below.

a. Line that passes through points $$A$$ and $$B$$

b. Line that passes through points $$B$$ and $$C$$

c. Line that passes through points $$C$$ and $$D$$

d. Line that passes through points $$D$$ and $$A$$

Guiding Questions

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Problem 3

Optional: Play the memory Matching Game with linear equations and graphs. Note that this requires some advance preparation.

Directions for students:

Find a partner and clear off your desks.
Separate the cards into a pile with equations and a pile with graphs.
Turn the equation cards over and organize them into rows/columns on one desk.
Turn the graph cards over and organize them into rows/columns on another desk.
On the first person’s turn, turn over an equation card and a graph card. If the cards match, then the player gets to keep the cards. If they do not match, turn the cards over in the same spot. The turn is over.
1. NOTE: If the player believes she or he has a match, then the player must prove that there is a match. The other player has the option to disagree and explain why. If the other player is right (and the first player was mistaken), then the other player gets to keep the card and then take a turn.
Repeat step 5 for the second player’s turn.
The game is over when all cards have been matched. The person with the most number of pairs wins the round. Another round may be played.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Write the slope-intercept form of the equation for each line below.

Student Response

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Problem 2

Marty writes the equation $${y=4x+2}$$ to represent the line shown in the graph below. Do you agree with the equation that Marty wrote for the line? Explain why or why not.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include spiraled problems of finding slope from two coordinate points.

Open Up Resources Grade 8 Unit 3 Practice Problems — Lesson 11
Kuta Software Free Pre-Algebra Worksheets Writing Linear Equations
EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic C > Lesson 20 — Exercises and Problem Set; note, some problems prompt students to write equations from slope-intercept form into standard form. This can be skipped.

Lesson 9

Lesson 11

Lesson Map

Topic A: Comparing Proportional Relationships

Review representations of proportional relationships.

8.EE.B.5

Graph proportional relationships and interpret slope as the unit rate.

8.EE.B.5

Compare proportional relationships represented as graphs.

8.EE.B.5

Compare proportional relationships represented in different ways.

8.EE.B.5

Topic B: Slope and Graphing Linear Equations

Graph a linear equation using a table of values.

8.F.B.4

Define slope and determine slope from graphs.

8.EE.B.6

Determine slope from coordinate points. Find slope of horizontal and vertical lines.

8.EE.B.6 8.F.B.4

Graph linear equations using slope-intercept form $${y = mx + b}$$.

8.EE.B.6 8.F.A.3

Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.

8.EE.B.6

Topic C: Writing Linear Equations

Write linear equations from graphs in the coordinate plane.

8.EE.B.6 8.F.B.4

Write linear equations using slope and a given point on the line.

8.EE.B.6 8.F.B.4

Write linear equations using two given points on the line.

8.EE.B.6 8.F.B.4

Write linear equations for parallel and perpendicular lines.

8.EE.B.6

Compare linear functions represented in different ways.

8.F.A.2 8.F.B.4

Model real-world situations with linear relationships.

8.F.B.4

Linear Relationships

Objective

Common Core Standards

Core Standards

Expressions and Equations

Functions

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Lesson Map

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