In this activity students work to understand the form of equations that will result in vertical or horizontal lines. In later activities in the lesson, students will be asked to write equations of horizontal or vertical lines that have certain properties. By making connections between the graphs and equations of vertical lines, students make sense of problems and persevere in solving them (MP1).

The purpose of the discussion is to ensure that students understand that, for a constant , the equation of the form  is represented by a vertical line and the equation of the form  is represented by a horizontal line.

Some questions for discussion:

• "Why is an equation like represented by a horizontal line?" (Because all of the coordinate pairs with a -value of 7 line up horizontally.)
• "How can you know from the equation alone whether it will be represented by a horizontal, vertical, or tilted line?" (Horizontal lines are all of the form , vertical lines are all of the form , and tilted lines will have both and in the equation (with nonzero coefficients).)
• “What is the equation that would match with graph D?” ( )

The purpose of this activity is for students to practice combining like terms for expressions that are similar to what students will see when solving systems of equations by elimination. Students will need to add or subtract expressions to eliminate a variable. This activity gives students the chance to practice that skill. Combining like terms to create equivalent expressions gives students the chance to reason abstractly and quantitatively (MP2).

In this activity, students solve a system of equations by graphing and then include a third—vertical or horizontal—line through the solution point. In the associated Algebra 1 lesson, students will graph equations in a system and additional equations that arise from the elimination method to show that they all intersect at the solution. As students represent the solution to each system of equations with a vertical or horizontal line, they are expressing regularity in repeated reasoning (MP8).

To focus on the work of the activity, it is recommended that students have access to Desmos or another graphing tool to more quickly and accurately find the solutions to the system of equations through graphing. If students need practice graphing lines representing equations by hand or if digital access is not available, the print version provides a graph with one of the lines given and asks students to graph the second line by hand.