Analyzing Linear Functions

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SWBAT understand the relationship between the equation of a linear function and the points that lie on a line.

Big Idea

Students analyze different components of slope-intercept form and use their observations to prove statements about lines and points.


10 minutes

As class begins, students will complete the Graphing Linear Equations Do-Now. Students learned how to graph lines in slope-intercept form during our first unit. I will prompt them to refer to their notes to guide them along if they have forgotten.  

The purpose of this Do-Now is to refresh student's memories of linear functions. I will use this time to see who may still need support with this prerequisite standard.

After about six minutes, I will graph each line on the board, while students grade their own papers at their seats. Students will write their score on the top of their paper, before passing them to the front of the room for me to collect.

Next, a volunteer will read today's objective: "SWBAT understand the relationship between the equation of a linear function and the points that lie on a line".

I will conclude the opening by asking a few volunteers to recall some things that we have already learned about a linear function.

Guided Notes + Practice

30 minutes

Using the Analyze Linear Function Notes, I will first ask students to label the slope and y-intercept of the equation on the top of their paper (y = 2x + 1). They should then graph the line on the coordinate plane provided.

Next, I will ask students to pick four points that are on the line as well as four points that are not on the line. Students should write the coordinates of the point beside it on the graph, as well as label the x 

The goal of this activity is for students to discover the relationship between the equation of a line, and the points that lie on the line. The secondary goal of this activity is for students to become familiar with true/false statements when proving the validity of a statement in math. I will guide students to this point with the following questions:

  • What do we already know about the line y = 2x + 1?
  • What is the slope of this line? How can you tell on the graph?
  • What is the y-intercept? How can you tell on the graph?
  • What two variables are still unknown in the equation y = 2x + 1.
  • Look at the four points that are on the line that you just plotted. What did you label them with? 
  • Let's see if the x and y that you labeled each point with have a relationship with the equation of the line.
  • Let's plug in the coordinates to the points you picked that weren't on the line. Do you think they'l produce a true statement as well?
  • Do you see a pattern?
  • Complete the same exercise with the line y = 1/2x - 4. Does the same thing happen with a different equation?
  • What conclusion can we make about points that lie on a line?


On the back of their paper, we will complete example one as a whole group.

Small Group Differentiated Activities

30 minutes

As a whole, students did not have too much difficulty verifying whether a point was on a line. Since the focus of this new unit is graphing linear equations, the second half of class will be spent ensuring that all students are fluent with this standard before diving in further. 

Students who scored 4/6 or higher on their Do-Now will complete the Abstract Art Activity independently. Students will create their own piece of abstract art by creating a graphing linear equations on a piece of graph paper. 

Students who still need help graphing lines in slope intercept form will work in a small group with the teacher, where we will use whiteboards and markers to practice graphing lines in slope intercept form.


10 minutes

I will ask a student to give a 15 second summary of what we did today in class. I will ask another student to elaborate on the relationship between points on a line and slope intercept form. 

Students will complete exit card. The exit cards should be graded directly after class, and the students should then be grouped by the percentage of correct questions for the small group activity to be completed during the next lesson.