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
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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.
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F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
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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
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8.EE.B.5
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8.EE.B.6
Criteria for Success
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- Rearrange a linear equation to reveal the slope when an equation is given in standard form.
- Substitute zeros for the appropriate variable to find the intercepts of a linear function.
- Write a linear equation given features of the linear equation.
- Graph a linear equation from all three forms of linear equation.
Tips for Teachers
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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
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Problem 1
Prove algebraically that point $$C$$ is not on the same line as points $$A$$ and $$B$$.
Guiding Questions
References
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
Problem 3
Write a linear equation that contains the points shown in the graph below.
Guiding Questions
Problem Set
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Open Middle Intercept Form Equations
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Desmos Match My Line
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MARS Formative Assessment Lesson for Grade 8 Defining Lines by Points, Slopes, and Equations
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This resource should be used for both Lesson 1 and Lesson 2.
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Desmos Polygraph: Lines
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Desmos Put the Point on the Line
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Open Middle Finding Intercepts
Target Task
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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.