The purpose of this Warm-up is to elicit the idea that certain elements of equations are visible in graphs representing them, which will be useful when students match graphs to possible equations in a later activity. While students may notice and wonder many things about these graphs, how you can see 5 and 2 on the graphs are the important discussion points.

This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is connections between an equation and its graph.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the equations and graphs. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the connection between the 5 and 2 in the equations and the graphs does not come up during the conversation, ask students to discuss this idea.

The purpose of this activity is for students to make connections between key features of graphs and equations in different forms. Students reason abstractly and quantitatively when making these connections (MP2). This activity focuses on linear equations, while the associated Algebra 1 lesson makes similar connections with quadratic equations. The form and parts of an equation can give us information about the graph of the equation: about the slope, the intercepts, or the position relative to the axes. Some forms allow us to predict features of a graph more easily.

• Slope-intercept form helps us name the slope and -intercept of the graph right away.
• The form can help us name the - and -intercepts. When either variable has a value of 0, we can find the other value fairly quickly.
• When the constant term is 0 (as in the form ), the graph goes through the origin.
• When the equation is a number, the graph is a horizontal line. When the graph is a number, the graph is a vertical line.

Monitor for students who use these different strategies:

• Make a quick sketch by plotting a few points.
• Reason about the - and -intercepts.
• Rewrite the equation to be in a form to easily see key features like the slope and intercepts.

In this practice activity, students analyze whether a few different equations could be represented by a graph, propose a new equation that could be represented by other graphs, and then interpret the meaning of the intercepts of a linear equation representing a context. When working on these problems, students look for and make use of the structure of equations and graphs (MP7).