Linear Equations, Inequalities and Systems

Lesson 2

Math

Unit 4

9th Grade

Lesson 2 of 14

Objective


Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.

Common Core Standards


Core Standards

  • F.IF.B.4 — For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • A.SSE.B.3 — Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.EE.B.5
  • 8.EE.B.6

Criteria for Success


  1. Rearrange a linear equation to reveal the slope when an equation is given in standard form. 
  2. Substitute zeros for the appropriate variable to find the intercepts of a linear function. 
  3. Write a linear equation given features of the linear equation. 
  4. Graph a linear equation from all three forms of linear equation. 

Tips for Teachers


Ensure that students have the general forms of all three major forms of a linear equation (standard, slope-intercept, point-slope) in their notes by the end of this lesson. 

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Anchor Problems


Problem 1

Prove algebraically that point $$C$$ is not on the same line as points $$A$$ and $$B$$

Guiding Questions

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References

Desmos Put the Point on the Line

Put the Point on the Line by Desmos is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Oct. 19, 2017, 2:32 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Graph the linear equation below. 

$${2x-3y=9}$$

Guiding Questions

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Problem 3

Write a linear equation that contains the points shown in the graph below. 

Guiding Questions

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Problem Set


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 linear equation has a slope of $$2$$ and contains the point $${(-3,5).}$$

  • Write the linear equation in all three forms. 
  • Graph the linear equation and verify that one additional point is a solution to one of the equations. 

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.

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Lesson 1

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Lesson 3

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions

Topic B: Properties and Solutions of Two-Variable Linear Inequalities

Topic C: Systems of Equations and Inequalities

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