Standard Form of Linear Functions
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Subject Area: Mathematics (B.E.S.T.) | Grade Level: 8
Lesson Length: 45 minutes
Keywords/Tags: Linear Functions
Lesson Description: Students have learned how to create and interpret linear equations in slope-intercept form from real-world scenarios. Now, they will create and interpret linear functions in standard form.

  • Other 8.FGR.5.6: Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function (e.g., rewrite a function expressed in standard form to slope-intercept form to reveal the slope of the function.rnrn8.FGR.5.9: Graph and analyze linear functions expressed in various algebraic forms (i.e., standard form, slope-intercept form, point-slope form) by hand and using technology; show key characteristics of the graph to describe applicable situations.
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Video : Graphing a Linear Equation: 5x+2y=20
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.")
Description: We can graph a the linear equation like 5x + 2y = 20 by rewriting it so y is isolated, then plugging in x values to find their corresponding y-values in a table. We can then graph those x-y pairs as points on a graph. Created by Sal Khan and Monterey Institute for Technology and Education.
Reading : Standard Form Rules for Linear Equations
Instructions: Please read the following article as many times as needed (aloud and silent) before starting to go through the rest of the lesson pages. Understanding the content of this passage is very important since the following lesson activities will be all about this content. Feel free to print the article if needed.

Summary of Standard Form Rules for Linear Equations:

  • Must have the form Ax+By=C.
  • A, B, and C must be integers (not fractions)
  • A can not be negative.
  • A, B, and C should have no common factors other than 1.

Description: What is the standard form of an equation? Learn the rules to convert an equation into standard form and view examples of how to rewrite equations in standard form.
Video : Graphing Linear Equations in Standard and Slope-Intercept Forms
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.
Description: Defining and Graphing Linear Equations written in Standard (Ax+By=C) and Slope-Intercept form (y=mx+b). Standard form is graphed by finding the x- and y-intercepts. Slope-intercept is found by plotting the y-intercept and using the slope to find the other points.
Quiz : Graphing Linear Equations in Standard Form
Instructions: Please complete this quiz by choosing the correct answer for each question. You can take this quiz as many times needed.
Question #1
Standard form is written as Ax+By = C
Question #2

What is the slope-intercept form of a line?

Question #3

Find the x and y intercepts of 4x - 5y = 40.

Question #4

Which ordered pair could represent a y-intercept on a graph?

Question #5
What is the y-intercept of
2x-5y=35?
Question #6
Find the x-intercept of 3x + 8y = 24.
Question #7
You need at least three points to graph a linear equation.
Question #8
Identify the slope and y-intercept of the linear function y - 4x = 2. 
Question #9

Which of the following linear equations is written in standard form?

Question #10

Which of the following is NOT written in simplified standard form?
 

Description: Students can graph linear equations in standard form by rewriting the equation in slope-intercept form, or finding the x and y intercepts, and graphing the points.
Resources : Quizziz: Graphing Linear Functions in Standard Form
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson. https://quizizz.com/join?gc=74631394
Quizziz: Graphing Linear Functions in Standard Form
The STANDARD FORM of a line is written as Ax + By = C. The easiest way to graph a function is the solve for the x-intercept and y-intercept and graph the two points. You can also graph an equation in standard form by converting it to slope-intercept form. Once you convert the equation, you can graph the y-intercept and the slope.
Blooket: Graphing Linear Equations in Standard Form
Students will solve for the x-intercept and y-intercept to choose a graph that matches the given equations.
Description: ​The STANDARD FORM of a line is written as Ax + By = C. The easiest way to graph a function is the solve for the x-intercept and y-intercept and graph the two points. You can also graph an equation in standard form by converting it to slope-intercept form. Once you convert the equation, you can graph the y-intercept and the slope.
Forum : Forms of Linear Equations
Instructions: This discussion forum will have questions for students to respond to. Read the posted questions and respond to each. Students are responsible for posting one initial and two peer responses for each topic.
Forms of Linear Equations
Of the forms of linear equations that you've learned (slope-intercept and standard form), which do you think is most valuable? In the future, do you think you'll use one form more often than the others?
Description: Students will discuss the forms of linear equations they have learned so far. The forms are slope-intercept form and standard form.
Assignment : Odd One Out

Determine which linear equation is the “odd one out” by finding the equation that does not have the same x- and y-intercept as the others!

A.  6x - y = 4

B. 5y - 30x = -20

C. 4y - 24x = 16

D. -3y + 18x = 12