Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 13
Math
Unit 5
8th Grade
Lesson 13 of 15
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Write linear equations for parallel and perpendicular lines.
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.
The foundational standards covered in this lesson
8.G.A.1 — Verify experimentally the properties of rotations, reflections, and translations:
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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This lesson is a good opportunity to review and spiral in concepts from throughout the unit.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Use Graph A and Graph B below to answer the questions.
a. In Graph A, translate line $$S$$ 3 units up to create parallel line $$S’$$.
b. In Graph B, rotate line $$T$$ 90° clockwise about the origin to create perpendicular line $$T’$$.
Lines $$L$$ and $$M$$ are parallel. The equation of line $$L$$ is $${4y=x}$$. Line $$M$$ passes through the point (0, -5).
What is an equation of line $$M$$?
Proportional relationships, lines, and linear equations, accessed on Feb. 24, 2018, 10:19 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Line $$P$$ passes through the points (0, 5) and (4, -3).
Line $$Q$$ is perpendicular to line $$P$$ and passes through the point (8, -2).
What is an equation for line $$Q$$?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Line $$A$$ is shown in the graph.
Write an equation for line $$B$$ and for line $$C$$.
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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.
Lesson 12
Lesson 14
Topic A: Comparing Proportional Relationships
Review representations of proportional relationships.
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
Compare proportional relationships represented as graphs.
Compare proportional relationships represented in different ways.
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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.
Topic C: Writing Linear Equations
Write linear equations from graphs in the coordinate plane.
Write linear equations using slope and a given point on the line.
Write linear equations using two given points on the line.
Compare linear functions represented in different ways.
8.F.A.2 8.F.B.4
Model real-world situations with linear relationships.
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