In this activity, students practice recognizing the slope and intercepts of inequalities. Students apply their knowledge of linear equations to linear inequalities by looking for and making use of structure (MP7). This will be useful in the associated Algebra 1 lesson when students graph linear equations and inequalities.

The purpose of the discussion is to recall how to identify key features of a graph in an inequality and in an equation.

Here are some questions for discussion:

• “How did you figure out the - and -intercepts of the boundary line?” (I know that the -intercept the is the -value when is 0, so I solved for . Similarly, the -intercept is the -value when is 0, so I solved for .)
• “Is the graph of an inequality finished when you have graphed the boundary line? How is graphing an inequality different from graphing an equation?” (No, the graph of an inequality needs to show all of the possible solutions. Graphing an equation is finished when the line is graphed, but graphing an inequality in two variables includes the boundary line and shading to indicate all of the solutions.)
• “How would you graph the boundary line of an inequality that looks like ?” (I would start by plotting the -value as the -intercept and then use the slope, , to plot at least one more point.)

The purpose of this activity is to give students practice writing and graphing equations from situations. In the next activity and in the supported Algebra 1 lesson, students will write and graph inequalities. Students then assess the meaning of points off of the line in the situation provided and interpret whether those points might be valid in the situation. As students interpret their answers in context they reason abstractly and quantitatively (MP2).

In this partner activity, students take turns matching graphs of inequalities to their symbolic and verbal descriptions. As students trade roles, explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Monitor for groups who use:

• Whether the inequality is less than or greater than and whether the shading is to the upper left or lower right.
• Whether the equation is strictly less than or greater than, or less than or equal to, or greater than or equal to, and whether the graphed line is dashed or solid.
• Testing solutions in the situation, equation, and graph.
• The boundary equation to determine the correct graphed line.

Monitor for groups that struggle to make sense of the graphs involving a vertical or horizontal line.