Authentic Lessons for 21st Century Learning

Airplanes and Airstrips, Part 1

Writing Linear Equations: Graphs

K20 Center, Michell Eike, Sherry Franklin, Dy'Nelle Todman | Published: September 1st, 2022 by K20 Center


This lesson addresses writing linear equations when given two points or a graph. Students will use their knowledge of slope and y-intercept to analyze linear graphs and represent what they see graphically as an equation. This lesson also offers an opportunity to reiterate the meaning of slope and y-intercept, while placing emphasis on linear relationships being represented and modeled in multiple ways. Prerequisites for this lesson include identifying slope and y-intercept when given an equation or graph, graphing linear equations, and being familiar with the different forms of a linear function.

Essential Question(s)

How can linear relationships be represented in multiple ways?



Students activate prior knowledge and show what they know about identifying slope and y-intercepts from graphs and equations.


Students are introduced to writing linear equations through a Desmos Classroom activity, by acting as pilots and attempting to safely land airplanes on airstrips.


Students formalize their understanding of how to write a linear equation and reassess the equations they wrote during the Explore activity.


Students create their own airplane challenge questions, demonstrating their understanding of the relationship between the equation and the graph of a linear function.


Students write linear equations for other students' airplane challenges.


  • Note Catcher handout (attached; one per student; printed front/back)

  • Guided Notes handout (attached; one per student; printed front only)

  • Guided Notes (Model Notes) document (attached; for teacher use)

  • Card Matching handout (optional; attached; one per pair; printed front only)

  • Pencils

  • Coloring utensils (4 colors per student; markers, colored pencils, pens, etc.)

  • Student devices with internet access


10 Minute(s)

Provide students with your session code. Then, have students go to and enter the session code.

Introduce the lesson using screens 1–2 of the Desmos Classroom activity. Screen 1 displays the lesson's essential question. Screen 2 identifies the lesson's learning objectives. Review each of these with students to the extent you feel necessary.

Assign student pairs or ask students to find their own partners. Direct students’ attention to screen 3 and inform students they are going to complete a Card Matching activity.

After students start the card matching activity, press the orange plus sign on the dashboard to allow students to progress to screen 4. Inform students that this screen gives students feedback and shows how many cards out of 20 are correctly matched. If the screen seems empty, it is because there are not yet any correct matches, whether that is from a lack of attempt, guessing, or misunderstanding.

Bring the class back together and have pairs share with the whole group how they matched their graphs and equations.

To guide the class discussion, consider asking some of the following questions:

  • What methods did you use to match the graphs and equations?

  • How did you know which graph went with each equation?

  • What characteristics did you look for in the graph that helped you pick its matching equation?

  • What characteristics did you look for in the equation that helped you pick its matching graph?

  • Were all the equations in slope-intercept form? If not, how did you find the matching graph for that equation?

  • What is slope-intercept form?

  • What is slope?

  • What is a y-intercept?

Use student responses to determine if students need a quick refresh on slope or y-intercept.


20 Minute(s)

On the dashboard, press the orange plus sign to allow students to progress to screen 5. Have students watch the video, "Funny Plane Landings," by clicking the link on the screen. The video gives students an idea of what an airplane landing on an airstrip looks like before using the idea to work with linear functions in the Desmos Classroom activity. Ask students to imagine they are pilots. Do they think they could do a better job than the pilots in the video? Is anyone interested in becoming a pilot?

Share with students that pilots are tasked with landing airplanes in the center of a landing strip to ensure the safest landing possible. However, as they saw in the video, it does not always happen that way. Explain to students that they all have a pretty good knowledge of linear functions, and they will explore, as pilots, how this knowledge can help them land some airplanes.

Give each student a copy of the attached Note Catcher handout, then press the orange plus sign on the Dashboard six times to allow students to progress to screens 6-11. Direct pairs of students to use the Stop and Jot strategy and pause at the end of each screen to make notes on their handout. Encourage students to also use this space to write down any questions they have as they work through the screens.


15 Minute(s)

On the Dashboard, press the orange plus sign to allow students to progress to screen 12. This screen indicates that students are to set aside their Desmos Classroom activity to complete their Guided Notes with the class. Give each student a copy of the attached Guided Notes handout. Use the attached Guided Notes (Model Notes) document to help guide students in completing their notes.

Give each student four coloring utensils. Students could share four markers or colored pencils/pens. Have students use one color for everything on the page that involves slope. Have students help create an exhaustive list of what "m" equals in the cloud bubble. Using that same color, draw the decreasing rise over run stair-steps below the first line (under slope-intercept form), labeling the rise and run.

Now have students use a second color for everything that involves the y-intercept. Have students write "y-intercept" and its definition next to the "b" equals in the second cloud bubble. Use this same color to label the point (0, b) on the y-axis of the first graph.

Using a third color, have students label any point on the second graph that is on the line with the ordered pair: (x1, y1). Have students avoid labeling the x- or y-intercepts, as that could cause confusion later. Let students know that point-slope form can still be used if the point is the x- or y-intercept but that their notes should be clear that the point is not required to be an intercept. Use this same color to fill in x1 and y1 in the point-slope equation. Then have students use the first color to show the decreasing rise over run stair-steps like they did for the first graph but on a smaller scale. Lastly, have students write that the point (x1, y1) is any point on the line in the third cloud bubble.

Using a fourth color, have students color the word "Standard" and label the x- and y-intercepts: (a, 0) and (0, b), respectively. If the y-intercept is already labeled with the second color, that is perfectly okay. Now, have students make a note in the last cloud bubble that this form is the most user-friendly when looking for x- and y-intercepts.

Direct students’ attention to the back of the Guided Notes and model how to land the plane safely (how to write the correct equation of a line).

After walking through an example, ask students to look at the questions they may have written on their Note Catcher and ask any questions they still have. Use student feedback to determine if you need to model 1–2 more examples.


10 Minute(s)

On the Dashboard, click the orange "Stop" button; now students can complete the Desmos activity at their own pace. Direct their attention to screen 13 and preview the task.

On screen 14, students are to create their own airplane challenge for their classmates to answer. First, students click the "Make My Challenge" button. The activity prompts students to move the airplane and airstrip and then write the equation for a successful landing.

Direct students’ attention to the back of their Note Catcher handout: Plane Landing. Instruct students to use the first row to write their name in the first column and their work in the second column as they create their own airplane challenge. Remind students that this is a challenge problem, so think of something that will challenge their classmates.

After submitting their airplane challenge, students will see their classmates’ airplane challenges.


15 Minute(s)

Direct students to click on any of their classmates’ challenges and safely land the plane by writing the correct linear equation and entering it into the Desmos Classroom activity. Instruct students to use their handout to write the name of their classmate (or mathematician’s name) in the first column and use the corresponding second column to show their work.

Have students complete their handout by answering five challenges from their classmates. Use the student responses to determine if students need additional practice or are ready for the next topic.