Linear Relationships

Lesson 8

Math

Unit 5

8th Grade

Lesson 8 of 15

Objective


Graph linear equations using slope-intercept form $${y = mx + b}$$.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 8.G.A.1

Criteria for Success


  1. Understand that the lines of equations $${y=mx}$$ and $${y=mx}+b$$ have the same slope $$m$$.
  2. Understand that $${y=mx}+b$$ is the translation of the line $$ {y=mx}$$ by a vertical distance $$b$$
  3. 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
  4. 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


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


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.

$$y=2x$$

$$x$$ $$y $$
-2  
-1  
0  
1  
2  

$$y=2x+3$$

$$x$$ $$y$$
-2  
-1  
0  
1  
1  
  1. $${y=2x}$$ 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?
  2. What is the $$y$$-value of the $$y$$-intercept of each line? Where do you see this in the equations?
  3. What is the slope of each line? Where do you see this in the equations? 
  4. 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. 

  1. $$y={1\over3} x-2$$
  2. $$y=-3x+4$$
  3. $$y=-x$$

Guiding Questions

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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.

  • Include problems where students match an equation to a graph by matching slope and $$y$$-intercepts.

Target Task


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.   

b.   

Student Response

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Lesson 7

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Lesson 9

Lesson Map

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Topic A: Comparing Proportional Relationships

Topic B: Slope and Graphing Linear Equations

Topic C: Writing Linear Equations