The purpose of this activity is to develop questions about a design made of linear equations. Students make sense of problems and persevere in solving them when they work to understand the design and connect it to what they know about linear equations (MP1).

The goal of this discussion is to direct students’ attention to the variety of key features of lines they can look for and identify.

Invite several partners to share one question with the class, and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as “equation,” “solution,” and “slope.”

The goal of this activity is to identify the equations of lines in a design. Some of the lines show the -intercept while others rely on other points. As students use the skills they have developed to write the equations of the lines, they can look for and make use of structure (MP7).

The purpose of this discussion is to allow students to share their methods of determining the equation of each line. Display the design. Invite students to select one of the lines and to explain how they determined the equation. Here are some questions for discussion:

• “Did anyone find the equation for this line in a different way?”
• “Which equations were easier to write and which were more challenging? Why?” (The horizontal line was easy because I knew it would be a number. The equations where I can see the -intercept are easy because I do not need to follow extra steps to find the parts of the equation. The equations where I can’t see the -intercept are harder because I need to use the points I have and work backward.)