Linear Equations, Inequalities and Systems

Lesson 2

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. 

Anchor Problems

?

Problem 1

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

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 The Match Foundation, Inc.

Problem 2

Graph the linear equation below. 

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

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

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.