There are two mathematical purposes for this lesson. The first is to help students recall properties of linear relationships that can be seen in graphs, tables, and equations, and to connect the representations so that students can move from one to the other.
The second is to help students recall that what graphs and tables show are the solutions to linear relationships, and to help students understand that linear relationships in two variables have infinitely many solutions, even though not every ordered pair \((x,y)\) is a solution to the equation. Students who struggle often struggle to generalize the concept of solving an equation in one variable to making sense of the set of solutions to an equation in two variables.
In the associated Algebra 1 lesson, students are given a situation in two variables and they must find the value of one variable given the value of the other, create an equation to represent the situation, use technology to create a graph, and interpret each representation. Understanding how lines and tables represent solution sets of linear relationships will help students make sense of graphs of and solutions to linear inequalities, and later, to make sense of solutions to systems of linear equations in their Algebra 1 class.
Looking across representations also helps students to look for and make use of structure (MP7), as they consider the solutions to an equation in two variables and what features are visible across representations.
- Make sense of the quantities and relationships represented in situations, tables, graphs, and equations.
- Recognize the connection between a linear equation, a graph representing it, and the coordinates of points on the graph.
- Let’s connect different representations.
Use the same black line master from lesson 3 in this unit.