In this partner activity, students take turns describing graphs and use that reasoning to match graphs with equations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). As students work, encourage them to refine their descriptions of graphs by using more precise language and mathematical terms (MP6).

Monitor for students who match only one equation with each graph and for disagreements about which equation goes with which graph.

The goal of this synthesis is to make sense of how equations that look different can have the same graph. Once all groups have completed the Card Sort, ask previously identified students to share which equation they matched with Graph A. If students matched a different equation with Graph A than those previously shared, invite them to share their thinking, and allow students to clarify each other's thinking.

• ''Are students who matched more than one equation to Graph A wrong?" (No, more than one equation fits with Graph A.)
• "What does it mean for equations to be equivalent, and how does this relate to this task?" (Equations are equivalent if they have the same solutions, which means they will have the same graph.)
• "How are the multiple equations that match Graph D similar to and different from the multiple equations that match Graph A?" (The equations that match Graph A are in different forms; one is in form, and one is in form. Both equations that match Graph D are in form. The equations that match Graph D are multiples of each other.)

The purpose of this activity is for students to practice identifying the parts of a linear equation that affect specific features of its graph, specifically the slope and -intercept. This will be useful when, in an associated Algebra 1 lesson, students make connections between two-variable linear equations and their graphs and situations that they represent. As students identify the key features, they are looking for and making use of structure (MP7).

Here are discussion questions:

• "How do you find the slope and -intercept for the graph of a linear equation written in standard form like ?" (Solve for to find the slope, and then substitute 0 for to find the -intercept.)
• "The rate of change in a situation corresponds to what part of the graph?" (The rate of change corresponds to the slope of a graph.)
• "Why is it useful to know the -intercept and slope?" (The -intercept and slope can make it very easy to create a graph from an equation because we know the key features. Also, they are useful for understanding a situation and the relationships between each quantity involved.)

Keep the display to be continued in a future lesson.