Objective
Graph linear equations using slope-intercept form $${y = mx + b}$$.
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.A.3— Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Functions
8.F.A.3— Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Foundational Standards
The foundational standards covered in this lesson
8.G.A.1
Geometry
8.G.A.1— Verify experimentally the properties of rotations, reflections, and translations:
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that the lines of equations$${y=mx}$$ and$${y=mx}+b$$ have the same slope $$m$$.
- Understand that $${y=mx}+b$$ is the translation of the line$$ {y=mx}$$ by a vertical distance $$b$$.
- Define$${y=mx}+b$$ as the slope-intercept form of a linear equation where $$m$$represents slope and $$b$$represents the value of the $$y$$-intercept.
- Identify the slope and $$y$$-intercept of an equation in form $${y=mx}+b$$, and use them to draw the line that represents the equation.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
In Lesson 8, students are introduced to the slope-intercept form of a linear equation, and they see how it is derived from the proportional equation$${y=mx}$$. They use this form as an efficient way to draw the graph of a linear equation. In Lesson 9, students will encounter equations in standard form, $${ax+by=c}$$, and they will write these equations into slope-intercept form to graph them.
Lesson Materials
- Patty paper (transparency paper) (1 sheet per student)
- Ruler (1 per student)
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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
Two linear equations are shown below. Complete the table of values for each one and graph the lines in the same coordinate plane. Then answer the questions that follow.
 | $$y=2x$$
| $$y=2x+3$$
|
a.$${y=2x}$$ is a proportional relationship represented by a line through the origin (0, 0). In $${y=2x}+3$$, what impact does the “+3” have on the table of values? What impact does it have on the lines in the graph? What transformation is this?
b.What is the$$y$$-value of the$$y$$-intercept of each line? Where do you see this in the equations?
c.What is the slope of each line? Where do you see this in the equations?
d.Describe the graph of the line $${y=2x}-3$$.
Guiding Questions
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Problem 2
For each linear equation below, identify the slope and $$y$$-intercept and use them to graph the line.
a.$$y={1\over3} x-2$$
b.$$y=-3x+4$$
c.$$y=-x$$
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
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Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
In each problem below, determine if the linear equation is correctly graphed in the coordinate plane. If it is not, then describe the error and draw the correct graph in the space provided.
a.$$y=-2x+2$$ | Error: |
b.$$y=-\frac{2}{3}x+1$$ | Error: |
Student Response
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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 problems where students match an equation to a graph by matching slope and $$y$$-intercepts.
- Open Up Resources Grade 8 Unit 3 Practice Problems—Lesson 8
- Kuta Software Free Pre-Algebra Worksheets Graphing Lines using Slope-Intercept Form—Do not include horizontal or vertical lines.
- EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic C > Lesson 18—Exercises and Problem Set
Lesson 7
Lesson 9
